Thankfully, a lot of old games love to use global variables because you can't run out of stack space or allocatable memory. Modern games shy away from that because even the tiniest consoles these days come with gigabytes worth of RAM, even a memory leak has to be a gigantic firehose to bring the system to a halt.
It depends, on a system with no ASLR it's potentially still deterministic, but there are a lot of potential sources of non-determinism.