There are many many more options if you build your own system, and you can then be more flexible in terms of the components and the machine that you end up with. For example: are you looking to max out the graphics card? do you want to be able to upgrade said card relatively easily in a year?
The other piece of advice is to not get too hung up on definitions. The HTPC cases are going to be more like what you are looking for in terms of looks and are perfectly capable of being gaming rigs. Take a look at the Silverstone cases as an example, and this one in particular for a fit in a living room:
You might think that one is too big, after all it fits a standard ATX case, in which case you can check out the slim models etc. However, more space makes it easier to cool quietly and it looks just like an amp you might see as part of a normal home theater set up.
Silverstone are not the only game in town either, Streacom, Origen AE, Lian Li, Fractal Design have some amazing looking cases and more mainstream players like Corsair (the Bulldog is coming soon as of writing this) have options on the way.
In terms of pre-built systems places like QuietPC have been offering excellent (and quiet, of course) options that would certainly fit in your living room.
As to whether to stack your components, I would always recommend an air gap and no direct contact - even though the heat will generally exhaust out the back a lot of the small form factor units are going to radiate heat from the case directly.
I have cooked a wireless router while sitting on top of a PC and had overheating problems with an Apple TV for similar reasons. If you must stack, then always try to have the hottest component at the top.