I'm running an old game (WoW 1.12) using Wine. On the particular server I'm playing on the crowding of people can make the game chew up memory fast. I frequently get a crash where the error is "out of memory". How can I allocate more memory for a particular program run by the loader?
You cannot "allocate more memory for a particular program", that's not how Linux works.
You can either purchase and add more RAM to the server, OR use swap. Read
man mkswap and