Without knowing what video card you have in that machine a definitive answer is not possible, but if it is a recently purchased machine then most probably yes.
As for the other machine, its not the machine but the video card you have installed in it. You could probably update the video drivers for that card and the program would run fine again. ATI video drivers are iffy at best. Generally you need to try several different ones to obtain one that will work properly.
PS. Welcome to our forum.