The short answer is: No. 4 Gate is a powerful strategy with a lot of flexibility. This is because, as a race, Protoss is really dependent on their Tier 1 units. Since Protoss Tier 1 tend to be fairly tough units and a cheap caster, they can get away with this.
By comparison Terran Strategies are usually based around one of three different openings:
Each of which has its advantages. In terms of flexibility the 1:1:1 build gives you access to a wide arsenal of Terran units, but lacks the the synergy of upgrades, and thus relies on unit composition to make up. Meanwhile, Mech has very little flexbility and relies on the strength of Siege Tanks supported by Thor/Hellion to deal with Air/Melee. By comparison the 3 Rax has nice flexibility. I think this is the closest thing you're going to find to a 4 Gate equivalent.
The standard 3 Rax opening is: 2 Techlabs + 1 Reactor and producing 2 Marauder/2 Marine. Some of the nice tweaks to this are: Including Ghosts (great against Muta/Toss), Mass Reapers (powerful vs early game Zerg, with a transition into pure Marauder), Supporting with Siege Tanks (deals with most ground strategies), and even drops via Medivacs (powerful harassment and nice synergy with Stim).
By comparison, Zerg doesn't really have a nice normal build like these, though Roach/Hydra play is still fairly standard. Some people will say this is because Zerg adapt very quickly (all their unit production is shared), where as other might suggest that Zerg tech VERY slowly, and thus are forced to depend on their Tier appropriate units while trying to tech up.
I hope this helps.
So the quick Zerg transition is a myth (kind of like the Yeti or his North American cousin the Sasquatch); Zerg take just about as long to transition from one build to the next as every other race. Where this misconception comes from is the Zerg's ability to remax, very quickly, with a new army.
Now obviously, I could tell you about how you need to scout better, but as I've mentioned before I don't think that's much better than telling you to "play better," so instead I'm going to tell you what you did wrong in your replay:
You didn't build tanks.
I'm not saying there aren't other viable Terran builds, or that other units aren't good for a Terran, or that you won't need other units too, but against a Zerg its hard to do better than Siege Tanks.
I'm going to quote Day9 on this one (on SotG):
[As Terran] you need that strong Tank back bone.
While going Bio heavy has its merits, against a Zerg player (especially in mid to late game), you need a strong Siege Tank back bone to deal with things like: Roach/Hydra, Ling/Baneling, Ultralisks, Broodlings. Otherwise you're essentially giving up one of your biggest advantages: AoE. The entire reason a lot of Zerg players struggle mid-late game ZvT is because these Siege Tank back bones are unassailable. As a result the Zerg often feels he needs to pull off some sort of clever Nydus or Drop play to break that Siege Tank line (called, catching him out of position).
To augment your Tank line, there are a very large number of things you can build (Marines, Marauders, Hellions, Thors, Banshees, Vikings, etc), and this is where you start to customize yourself to what you're seeing from the Zerg (remember scouting). Against heavy Muta play, I tend to prefer Marines with a few Thors thrown in for range. A lot of Zerg will try to counter this with Ling/Baneling, but if you have that solid Tank line (and they're well spread out), you can usually handle that situation. On the other hand, if I'm seeing more Corruptor/Broodlord play, I want to have Vikings. Vikings are one of the few units you can really keep pace with Zerg production on (especially if he's dumping Corrputors into Broodlords). If I see Ultralisk, or Roach/Hydra. I like to back up my Siege Tanks with Marauders. While Siege do great damage against Ultra, its Marauders who are the real cost effective killers there. If you're starting to see Infestors, you need Ravens and Ghosts, so your Tank line doesn't get slimed.
But remember, you still need that solid Tank back bone before you stand a chance. I'm not saying build tanks first, but if you find yourself in mid game without a dozen or so Tanks, its going to be an uphill battle for you.
Best Answer
Ice Fisher by Spanisihwa sounds like the right build for you, it's a worked out Macro/Macro+:
It focuses you on building a strong two base economy, thus practicing your macro.
Be more dependent on scout information, which is important in 1v1. Know your opponent...
You need to be aware of this information, it allows you to know when to switch between building drones and building army. Placing some overlords and zerglings near the opponent in the right place to see incoming units is a vital thing, this gives you the right amount of time to produce the right amount of units.
In the end, you don't want to be over-producing army so that you have more drones for your economy; it takes some time to get it right put it pays off and may make the difference in the long end. A lot of beginning Zerg players don't focus on this aspect, imbalances them resulting in loss.
With only a subtle difference against Zerg, the build is safe and isn't dependent on cheese/rush.
With macro / economy comes learning to trade-off / adapt to the situation, hence proper play.
The defensive / FE approach of this build isn't always appreciated in team games, either your team rushes and you have to go along or they rush your front door and you are incapable of defending from two players simultaneously before your team mates arrive. Locks you to 1v1...
You can continue on this build after Gold / Platinum up to the Grandmasters. The problem lies not with the build, but it lies with execution of the build; don't expect magic to happen from Day 1, a lot of practice lies ahead with any build if you want to get at the highest levels, even when cheesing...
What is this build about?
By focusing on minimal defenses (enough to hold off your opponent), you excel in economy.
By focusing on minimal early gas, you come out ahead mid game as you take all four extractors.
Using static defense as well as queens (handy for early anti-air / creep spread / natural injection) and perhaps some slow zerglings, you make sure that you can hold off a rush at minimal cost.
An aggressive Zerg player in the later game; as there is a turning point where it becomes non-feasible to keep playing defensive (Zerg should contain, not be contained), it's important that one focuses on pushing rather than defending. Because of the high influx of minerals and gas, you'll be able to just throw tons of units into your opponents army as well as use nasty tricks to attack the opponent's bases from different sides.
Consider the time it takes to produce a Terran marine army, now consider the amount of Zerglings you can throw at him if you are on three bases and perhaps also have two macro hatcheries. You'll simply outnumber him... ;)
I'm not going to list the build here, as you need to research this yourself. Looking through the TL thread, watching his gameplay a few times (Day[9] perhaps?) and then go and practice it yourself.
Working out how to transition out of the build completely depends on the game, a nice thing to do is to keep notes (As simple as Notepad, perhaps Evernote or OneNote; some people even use Excel) in which you list the specific problems you have with your build and figure out what transition works the best against them.
For example: Are enemy infestors a problem? Consider:
How did he get to this point in his build? Did I miss an opportunity to scout & stop him earlier?
Why don't I have the right units yet to combat this situation? Did he sneak by or were I too late?
And you'll eventually know when to scout that he is going infestors and be ready to transition. As there are a lot of possible transitions, it would be unfeasible to list all possible situations...
As a conclusion, this might not be the most straight-forward build but it'll sure leave you with a good view on economy and macro before starting to work out more towards the micro aspects of the game.