Kinda late and perhaps the fix only works for me, but run the 64bit version directly from the game folder. Directory Crysis\Bin64\Crysis.exe
There's also a Crysis64.exe, but I run the former mentioned as administrator and works fine like that. Also, check the Remastered Trilogy on EA App. It didn't add to my library by default, but mentioned that it was available to redeem due to my EA Play subscription.
For me, I'm playing the 2007 game, having played the Xbox 360 port because I wanted to play with controller, and then finished 2 and 3. The Xbox 360 port and Remastered Crysis lack some content, like a mission some people said was unnecessary, in case the information serves you any purpose.