have them set their vid quality levels lower.
Turn off shiny water
Turn off animated textures
Turn off environment mapping on creatures
turn off Visual effects high.
Basically, set it as low as possible, then slowly, one item at a time, re-enable each of those features. I mean, re-enable one, test it by loading the area, if it works, re-enable the next one etc.
Most likely though, you will have to send them to the technical-self-help forums here, and have them research their vid card and drivers, and/or operating systems. Most likely vid card related though.
Several of Worm's tilesets are high poly sets, increasing the workload on the player's pc. It may also be the fact that most of the tiles in his sets are not compiled, which increases the workload on the vid card, and ATI graphics cards hate working hard. If the tiles are not compiled, the graphics card has to perform the math to compile them. Nvidia typically handles these things better, but even with NVidia, the specific driver version can cause issues
The only other possible issue would be area size, and/or number of placeables in the given area.