How well will a 256mb ATI Radeon X1600 play this game?

Does R:TW require a powerful video card?

No, it runs ok on slow video cards like the 66xx series. It runs very good on the 6800gt/ultra and faster cards with AA/large unit size/high settings.

MTW2 has higher requirements will definitely need a beast if you want to turn up the graphics settings.

I have a Sapphire Radeon X700 and it runs RTW great, so an X1600 should fly along.

I have an intergrated 6150 and it runs RTW great. Your x1600 should have no problems at all, even at higher settings.