When you're having game performance issues, the first thing to try is always to set all video options to lowest. From there, you can gradually increase individual settings up to the point where they negatively impact performance.
CrossOver on the Mac uses the resolution requested by the game to determine whether it should go into full-screen mode (hiding the menu bar and Dock) or not. There's one "magical" resolution which is non-full-screen; all others are full-screen resolutions. The non-full-screen resolution is your normal desktop resolution with the menu bar excluded -- that's 22 pixels subtracted from the height. (If you have multiple displays, the non-full-screen resolution is the smallest rectangle which fully contains your whole desktop area. In that case, you can't necessarily look for the 22 pixel height difference, but it should be pretty obvious which resolution is way bigger than any one of your displays.)
For example, my display is 1920x1200. In a game, that resolution will be one of the possible choices, but so will 1920x1178. If I select 1920x1200, CrossOver will go into full-screen mode. If I select 1920x1178, the game will think it's in full-screen mode, but CrossOver won't hide the menu bar or Dock.
This is mostly a side-effect of technical design decisions, but some people find it useful. Maybe they keep their Dock hidden or on a second display, and they like the flexibility of being able to see and activate other applications while playing a "full-screen" game.
One can always force CrossOver out of full-screen mode using Command-Option-R, which is the keyboard shortcut for the Restore Display item on the Window menu. Again, the game won't be aware of this, but CrossOver will unhide the menu bar and Dock and let you switch away to other apps.