The amount of video memory (or type of video chipset) you have has little impact on video editing. The exception is for lower-end or integrated video graphics that use main memory for video RAM.
I've edited video on a computer with 512MB RAM and integrated video which used 64MB of main memory for video RAM. That left 448MB of RAM for Windows and other programs. It worked fine.
The Radeon X300 SE 128MB HyperMemory has 128MB of on-board video RAM and can use up to another 128MB of main memory as video RAM for a total of 256MB. (Explanation of HyperMemory technology
.) The amount of main memory used by the video card will vary depending on the task so at times you might have all of your system RAM available for programs.
Example 1 (assuming the computer has 512MB of RAM): basic web browsing isn't very graphics intense so the card won't need more than the on-board 128MB of video RAM. So all 512MB of RAM is available for the OS and programs.
Example 2 (assuming the computer has 512MB of RAM): playing a fairly graphics heavy game means that the video card needs more memory to function at peak levels. It will use 128MB of main memory as additional video RAM which leaves 384MB (512 - 128) of RAM for the OS and programs.
Increasing the amount of main memory will be pretty beneficial to overall performance in any system (to a point), but more so in a computer with a video adapter that uses main memory for video RAM.