I don't have all the technical know how/answers but I believe AMD licensed 64-bit instructions to Intel (something like that and don't kill me if I got it wrong) anyways whether it say AMD or not if it's 64-bit it will run on Intel processors. Don't get caught up in the AMD part of it.
Anyway if you do decide to use the 64-bit patch don't patch Far Cry to the 1.4 patch, it results in strange issues. This is from experience
And yes, I have Far Cry running on my system with the AMD 64-patch
As for Crysis - just install, patch and play. It's that simple nothing special needed to get it to run..... other than your hardware as the game is STILL system intensive. And as noted, the game has native 64-bit support