It IS the roast that is the difference. The only real difference in the beans is that some beans taste better at a higher roast than others, so they are more appropriate for espresso. Your Italian grocery coffee company may be using the espresso label for marketing purposes, but in general, espresso coffee beans can be the same beans that are used for "regular" coffee, but roasted to a French or Italian roast level, which is darker than City or Full City.
Since the advent of Starbucks, many roasts are much darker than they used to be. Dunkin' Donuts coffee, which is a Full City roast, used to be the norm, but now a French seems to be what you can buy.
I roast my own coffee and take it to just into the second crack which is, generally, a Full City roast...a point where the character of the coffee predominates rather than the flavor of the roast. There is more information about roasts at Sweet Marias where I buy my green beans, and reading through the site will give you way more of a coffee education than you probably ever wanted.
So, yes, you can use the coffee you have to make brewed coffee. It will probably be roastier than you would normally have, unless it is just a marketing ploy, in which case it will taste normal. Consider how long you have had this coffee; if it has been shelved for a while "normal" probably won't be all that great, since freshly roasted coffee is, generally, way better than old coffee. But as long as the oils aren't rancid, it is more likely just going to be bland.
If you have a grinder and don't have a coffee pot, here's what I would do (I'm assuming you don't also have a coffee filter):
Step 1 - Grind the beans. If you have a grinder, grind your beans until you have a medium grind:
Step 2 - Punch a couple of holes into the bottom of a disposable, hot-beverage cup (or a tin can)
Step 3 - Line inside of cup or can from #2 with a handkerchief. Secure edges of handkerchief around lip of cup with binder clips or a rubberband.
Step 4 - Place grounds into cup. 2-3 tablespoons should be enough.
Step 5 - Place cup over top of empty mug (so coffee can flow into it)
Step 6 - Pour water (very slowly and over all the grounds) that is 5 minutes off the boil over coffee grounds.
You can view a similar tutorial here.
Best Answer
The simplest answer is: buy the Pike coffee blend from Starbucks, they sell their beans.
Brew it at home with any method you prefer. The coffee maker you use is a matter of preference. Starbucks themselves use a large drip pot, which is the most common home type.
If you want to avoid using Starbucks beans, from the description of the roast (I haven't tasted it in quite a while, and it didn't make an impression), it sounds like a mountain grown coffee, something like Kenyan would be a good choice. Since they describe it as low acidity, I am guessing that it might be somewhat less over-roasted than Starbucks coffee usually is, so I would suggest a Full City Roast, or perhaps a Vienna roast.
Its certainly a blend, so no single bean will replicate it. I would suggest finding a blend from a reputable coffee roaster that you like, or simply buying the Pike blend from Starbucks.