I have an HTC Desire SV, which has almost the same specs as Desire X. The problem is I'm unable to install HD games, since the phone storage has only 800MB space.
I have gone to Settings > Apps and checked for the option to move to SD card but there are only 2 options available move to phone and move to internal.
I cannot play games like Max Payne; it has cache files around 2GB. Since the cache is too big for the phone memory, I cannot install it.
How can I install games like Max Payne?
Thing is: you can't, obviously, as you don't have enough internal storage.
If your device is rooted, however, there are ways to work around this storage problem. You can fool your device by linking/mounting a partition on your SD card to be used as "fake internal memory". But while this would work-around the underlying issue (not enough storage), the Playstore still would refuse to let you install those apps, as your "official phone specs" have not been changed. If you could get hold of the .apk, however, you might be able to side-load (manually install) it. Also, having root, you could manipulate the system file responsible for this (build.spec?), fooling the playstore into thinking your device would be a Desire X (or whatever you chose).
So you see there might be work-arounds, but they are not easy to apply. Without rooting your device (and thus most likely voiding your warranty if you're living outside the EU), it simply is impossible AFAIK.
