Well -- it doesn't require a large screen to play(*). I think for most people it requires a large screen to be fun. Lots of exceptions, of course (especially good eyesight, already hooked on Warcraft, lying in bed with the laptop screen a foot away, specialized interests in Warcraft where the screen size doesn't matter much, etc.) I would expect most people starting warcraft to have similar reactions to yours on a small screen.

That said, the camera zoom, angle, etc. can be adjusted, and I mentioned shift-V above to toggle the type of nameplate display.

(*) There are some specialized cases involving playing in groups where you really *need* a large monitor. But those aren't things you'd do just starting out.