The Game is 7 years old and was written for the OS you mentioned and is therefore listed as compatible for this operating systems.
That doesn't mean the game will not run on Windows 8.1 or Windows 10, as a matter of fact it does run most of the time without any problems on this operating systems.
I'd just like to say that I'm running Mass Effect 2 just fine on my system with Windows 10 Home Premium 64 bit. I have had to make the point of running the clean boot to install the game and all of the content without issue, and found it preferable to activate it in clean boot as well (running it for the first time, and signing into the irritating Cerberus Network for the first time). It should also be noted that there's been a large number of issues with what character's are acceptable for passwords, so I generally just recommend either trying out the character's stated to be acceptable in this thread here (linkage!) or go with a pure alphabetical upper and lower case string comboed with 1 through 0. Again, I do believe you only need to go through the whole irritation of the clean boot and install (possibly with a repair/update) on the first go round, after that all should be well. Oh, ALSO! DO NOT ATTEMPT TO CONFIGURE THE GAME WITH THE CONFIGURATION TOOL IN THE GAME FOLDER! Set up your audio & visual preferences in the game itself. And be aware that the game has some odd dual use of ME2Game.exe and MassEffect2.exe which I never really got, but ... I basically (with an AMD card) create 2 profiles in AMD, one for ME2Game.exe and one for MassEffect2.exe. It's extra work, but if you want some of the benefits of a GPU Profile for your game, worth it (I think).
My 3 cents. 🙂
Edit: Just in case, a clean boot requires "Run -> "msconfig" -> Services Tab -> Check 'Hide all Microsoft Services' -> Disable All & Apply -> Startup Tab and 'Open Task Manager' -> Disable absolutely everything in 'Startup' tab. Close, hit apply again if need be, and 'ok.' A prompt should appear and you should just agree to restart immediately. When it boots back up, pretty much nothing will be running that will interfere with the installation.
Edit: The URL in the link below this line
