How to play Worms Armageddon on Windows 7

It's actually quite likely that these games are relying on old 16-bit DLLs. A lot of early 32-bit software relied on old 16-bit DLLs for some functions, as they did the job, they weren't used in a performance critical part of the software and there was no need to look for 32-bit versions. (for example until fairly recently the install software was often 16-bit, so much so that Win7 actually detects that and silently replaces with it's own 64-bit version of the old DLL).

Have you looked at Windows 7's XP Mode? This runs an entire copy of 32-bit Windows XP within your Windows 7, letting old programs run within XP without the program knowing it's on a 64-bit Win7 machine at all, and as it's all integrated you will hardly notice that it's running in XP.

Windows 7's XP Mode: what it is, how it works, who it's for

Could this be the same type of issue that affects other RTS games?

Try closing Explorer.exe either before running the game, or right after it starts.

Here is a question that is asking about older RTS games: How do I get an older Windows 95/98 game to run in Windows 7 64-bit without some colors looking off?