Instead of letting wine detect the amount of video card memory available, you can explicitly set it with winetricks. This can sometimes work, and is a possibility, as is investigating the other graphical tweaks available with winetricks.
You can run the following, for example, to set the videomemory to 512, rather than let wine try to detect the video memory available:
winetricks videomemorysize=512
It is important to note that this will affect the default WINEPREFIX ($HOME/.wine) only. If you have other wineprefixes, you will have to specify your particular WINEPREFIX; for example:
env WINEPREFIX=$HOME/.otherprefix winetricks videomemorysize=512
You can also use the gui version of winetricks from the applications menu and select the wineprefix and then select change settings. Other options available for setting video memory are:

There is no way to tell whether these settings will work with your system, and you may have to tweak other settings such as shaders, etc. I should refer to the wine appdb page and the winetricks wiki and wine FAQ. You may have to investigate how wine and wined3d is detecting your video card and its capabilities.
It also might be worth reinstalling and using a fresh WINEPREFIX, as that can sometimes solve problems (see my answer here for how to do that), as well as using the current development version of wine from the official Ubuntu wine team ppa.