No, that's not it. Porki put his game there, and it works.
Windows can handle 32bits and 64 bits programs just fine. There was never any need to split the Program Files directory by architecture, but Microsoft did it anyway.
The thing is that "C:\Program Files (x86)" is the garbage dump where all the misbehaved programs install their crap. There's no rule in this folder, it is a free-for-all where every installer does whatever it wants. Microsoft had to go to great length to not interfere with anything that's put in there.
If you care one bit about your game, you don't put it with the garbage, you keep it safe and sound in another folder, even another drive if you can.