Not quite as invisibility since it has its own caveats, emphasis mine.

You are also adept at evading creatures that rely on darkvision. Such creatures gain no benefit when attempting to detect you in dark and dim conditions. Additionally, when the DM determines if you can hide from a creature, that creature gains no benefit from its darkvision. UA: The ranger, revised P. 8

The main difference is that, invisibility does not end when you are detected by other means that are not magical or with special senses but, in the ranger case, the condition/ability ends as soon as the ranger is detected.

The invisibility condition in PHB 191.
An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature’s location can be detected by any noise it makes or any tracks it leaves.

Attack rolls against the creature have disadvantage, and the creature’s attack rolls have advantage.

Now, about detection; attacking or casting a spell make you lose the benefit as stated in PHB. 195. Also, there is a big difference between dark and dim conditions (PHB. 183). The main difference is that with normal sight you can see the ranger in dim conditions but you are blinded in dark conditions. Therefore, the ranger in dim condition is not treated as if it has invisibility/heavily obscured, the ranger is treated as if in dim condition.

(PHB 195) If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses.

(PHB 183) A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition.

Thus, against the ranger when trying to detect him in dark or dim light condition, a Dark Elf and a Human are not treated differently, as if they have the same visual capacities.

As an example, by courtesy of Keithcurtis; Robbie the Ranger and Frank the Fighter are trying to sneak past Danny the Drow and Harry the Human in a dimly lit cavern. Harry has disadvantage on the opposing perception on both the sneakers, while Danny only has disadvantage against Robbie the Ranger.

You remain invisible - but not because of the dagger

Let's look at the situation you are describing. We'll assume you are in an environment that qualifies as non-magical darkness and are fighting a creature with darkvision.

In this scenario, umbral sight is what matters.

You are also adept at evading creatures that rely on darkvision. While in darkness, you are invisible to any creature that relies on darkvision to see you in that darkness.

It does not state that you lose the invisibility after the attack. This is an always-on ability that happens in this type of environment.

Whether or not you hit, miss, or do anything else doesn't matter. You will always be invisible and unseen in this environment (unless something changes.)

In other environments, it may matter

The text of the dagger dictates that it only makes no sound when you hit or cut. If you miss, the dagger 'sounds' normal. How this plays out will likely be up to a DM.

Interaction with being Hidden

Since you quoted the rules around being hidden, let's address that case.

Your ranger is in darkness and has taken the action to Hide. Your roll is sufficiently high to beat the passive perception of your enemy. You are now Hidden and invisible. Very cool!

Now, you take out your dagger and attack (with advantage)!

You roll and miss - hidden has ended

As the dagger makes a normal noise, you lose your hidden status but remain invisible. As you've quoted, the dagger's special soundless property doesn't engage when you miss, only if you hit or cut.

At this point, the enemy knows your location and can attack it with disadvantage because you are no longer hidden (but still invisible.)

You roll and hit - up to a DM

Here is what it gets a bit trickier. The rules talk about being hidden as unseen and unheard. However, they also follow up with:

...you give away your location when the attack hits or misses

Normally, you'd give yourself away at this point and lose your hidden status (but still remain invisible.) What's tricky is you are still invisible (unseen) and because you hit, the weapon didn't make a sound.

I hate to say it, but in this case it's going to be a up to a DM as to whether you lose your hidden status. A DM can rule that while the blade makes no noise, you do (because you can still make noise even if the blade doesn't.)

That ruling does seem to take away from the weapon's properties though. A DM could instead rule that because the weapon is soundless and you are invisible, the attack doesn't give away your location and you remain hidden.

Because you are still hidden, the creature has to guess your location and still make an attack at disadvantage. If you've moved away (with no Opportunity Attack because you aren't seen), then they are very likely to not hit you unless they luckily guess your location.