I did a small test with Yozy today, and managed to play a level of Tyrian two-player via steam remote play.
What was needed:
Dosbox (I used 0.75 dosbox staging)
A steam game with remote play (I used lego star wars).
The basics are, install the game, remove it from the folder and copy in dosbox, and rename the executable ($game).exe. You will need the -noconsole option.
Then I just invited someone to play (Yozy), and played in full screen mode. He found the keyboard better to control with vs. the mouse.
YMMV, questions here, or on IRC.