I'm pretty sure he's on centred timings, that is it shows display modes lower resolution than the screen by showing them in the middle of the screen at the native resolution instead of scaling them.
In that case he should still be able to play the game, just not as desired through, but he said he can't play the game...
Hope your right through, as that would be easy to fix then.
If the Dosbox setup doesn't use a scaler, that means he'll be running 320x200 on a monitor designed for 1366x768 or higher. That's likely pretty unplayable especially for some. I've bad a couple of games do this to me on my laptop. Small picture, the rest is black.
A good starting suggestion to verify this though would be "Please hold down Alt and press enter
" This should force the game into a window on the desktop. If the game goes into a window and is the same size, then yes it looks like either the graphics card settings might need tweaking to ask it to nicely scale the game, or the dosbox configuraton file could in fact have been altered (for Mac?) to run fullscreen at the native resolution, but still not use a scaler. This, I believe, should also cause this, gfx card settings or not, since Dosbox is actually running the game in 1366x768. It's just not got enough graphics data to fill it out.
But as far as I can tell, the only way to get Dosbox to stick in a higher resolution than the game is outputting is by specifying fullresolution=<resolution> in the .conf file for the game. Might be worth a look though.