It might be possible to guesstimate the available memory: http://delphi3d.net/articles/viewarticle.php?article=texman.htm
quoting from the article:
The implementation of the glAreTexturesResident() function, which is so critical for this technique, has not been properly standardized. [...] This makes the technique described in this article pretty much useless - unless you want to put "NVidia 3D cards only" in your app's system requirements.
Not to mention that, especially with accelerated compositing, that the size of textures that could fit could be significantly less than the amount of VRAM the card has.
Isn't the amount of _free_ vram what wine really is interested in? The information how much RAM the card has is pretty much useless.
The amount of free VRAM is rather volatile. Most games would use the total amount of VRAM as a guide to how much to attempt to put onto the card, not as an absolute "this is how much you have to work with". Besides, if the specs for a D3D function say it returns the total amount of VRAM, WineD3D would need to return the total amount of VRAM.
Something you maybe could try, if you can determine the location of the X log file..
An nVidia card with the proprietary drivers:
# grep VideoRAM /var/log/Xorg.0.log (--) NVIDIA(0): VideoRAM: 262144 kBytes
A built-in Intel card with the open-source drivers:
# grep VideoRAM /var/log/Xorg.0.log (--) I810(0): Pre-allocated VideoRAM: 7932 kByte (==) I810(0): VideoRAM: 65536 kByte
I couldn't find anyone with an ATi card to test with, unfortunately.