It's not the graphics memory that's the culprit... it's the graphics chip itself. I did a test awhile back and was able to run the game on an older (another Compaq, this one from 2001) P4 laptop that only had a 32MB video card and it was pretty smooth - the memory was dedicated specifically to the video card, and it was an ATI-made chip (a Mobile radeon 7500, to be exact). Intel has always made a poor integrated graphics solution with the most barebones of capability... and they still advertised it as "great for gaming." Only with their newest chip (Sandy Bridge) have they got anything that remotely competes with the discrete solutions (AMD, NVIDIA).
I've got a couple of theories why the game does so poorly on the intel chips. One is that the chip might acually be able to process the relatively simple graphics of the game faster, but it requires some programming techniques/optimizations that BW is not aware of, since the cheaply designed card might use some non-standard functions to get the job done. Another is that it is a limitation of the BlitzMax engine that BW is using to create the game. Resolving either one would require time and resources that are likely not available to BW as an indie developer.
I will say that your dungeon performance should fare better... there's a lot less to be drawn on the screen, which always means a performance boost.
"Apparently, getting your ass kicked is now part of this complete breakfast." - Roy Greenhilt