Program Files is generally where 64bit programs get installed by default, and Program Files (x86) is where 32bit programs
get installed by default.
Games/programs will install to whichever of the two folders is appropriate if you allow them to install to the default location.
The vast majority of games are 32bit, only a relatively few newer games are 64bit (or exclusively 64bit. Some have .exe's for either).
- However, If you have another Partition, or HDD/SSD you can install your games there as well.
You can also create a new folder in C:\ and install your games there.
There is no benefit installing games and most software to the Program Files folders. The only software I install to the default
locations are my Anti-Virus, Browser, graphics drivers, and anything else I think may integrate closely with Windows.
The main advantage to installing games on another Partition/HDD is that the default Program Files folders are system protected folders,
and installing games in them has been known to cause permissions issues in the past with games that can be modded.
Installing games to a folder you create in C:\ just for the games, if you have no other option, also makes for better house keeping
and it is easier for you to find the game folders should that be necessary.
Another benefit to installing to a separate HDD is it makes doing a backup clone of your Windows drive\partition quicker,
and if using a small SSD for Windows (C:\), installing games to another HDD prevents the SSD from quickly filling up.
I also install my Steam (and games from Steam), Origin, UPlay and EPIC client software in their own folders on another HDD/Partition.
btw - There is no real benefit installing games on an SSD vs HDD other than a very few seconds quicker loading time.