There currently is a software that calculates if a computer can run a certain game on a website. This website does not work on mobile or tablets. Is there a way that can check if a smartphone can run a certain game? I'm talking Android and IOS.
Windows phone is discontinued, Microsoft don't support it anymore and I doubt people are making new games for it.
For Android a good rule of thumb is checking your phone version with the minimum required version of the game. If those match then you're good.
There isn't one program on all platforms to check for what you're asking.
can't say for sure about iPhone but possibly same as Android.
On mobile all you need to do is check that enough memory (ram) is available to run the game (/app). If you want to test your graphics then you have many applications to do that very well - im using Antutu on my android device, its totally free. Sometimes, if your graphic card is good and the memory should be enough, games still wont work well duo to bad operating system (old versions) or lack of permissions. good luck.