It's the height. So even if I got a higher resolution I wouldn't be able to shrink everything and see more?
Nope. The only thing that might change things a little is going from 16:9 to 16:10. In some games, like Starcraft, 16:9 shows more of the screen, but others might give you more from 16:10. It's more likely, given that they are both Blizzard games (Dota2 is written using Warcrafts engine), that 16:9 gives more viewable area on the sides. 1080p and 1440p are 16:9, 1920x1200 and 2560x1600 are 16:10.