That's where you're technically incorrect. If you have no interest in gaming, then video memory means nothing. What video memory does is allow games to load textures into the video RAM so that it's right there for the GPU to use. If you're not using the computer for gaming, you won't be loading textures. No textures == no need for large amounts of video RAM.
If you're using it just for basic computer use, viewing videos, basic computer use, almost -any- modern integrated graphics set would be sufficient, or if you have a CPU that doesn't have integrated graphics, any of the modern low end (ie: Radeon R7-240 or R7-250) would be more than adequate for the task. What you're going to need to look for is connector options more than video RAM. Just make sure that it comes with the connector needed (ie: HDMI, DVI, VGA etc), and look for the best price - currently R7-240's are running about $60 on eBay and it'll easily drive dual monitors