The game vote is in the write-in.
I'd point out that the story post suggests some time has passed since the game was decided and started (well, in the case of D&D the teaching of how to play being started). As such harry wouldn't just be about to start teaching the rules, he's either be partway through doing so or have already done so (not that that innately means Draco couldn't join in).
That said, I personally figure that Draco has not yet done enough to dissuade Harry from being nice and giving him a chance (and no one has yet pointed out to him the stigma the Malfoys have), not to mention two of Harry's friends indirectly made fun of Draco (even if only laughing because of a poor choice on how to introduce himself). As such I could see Harry at least giving him a shot as something of an apology. And if he is really being a dick he can be regulated to a sucky role like party healer or some such. I would also point out Dumbledore and many of those that follow his lead would be in favour of trying to sway Draco away from his family's viewpoint while he is in school. After all, just because his family is Dark, doesn't mean he has to turn out like them.
Still, all the valid reasons not to immediately turn down Draco aside, in all honesty I really just want to see him get hooked on D&D and start obsessing over the muggle game. Because even if Harry doesn't end up close friends with him, causing that would be hilarious. Also we should totally see if we can't start up a d&d (or possibly a generic RP) club. Would be a great way to hang out with friends that may end up in different houses, and could allow us to interact with and potentially influence Draco if we don't become friends with him here and without needing a super close relationship (after all if he is just another club member it won't put us strongly at odds with other friends who can't stand him). Thus potentially appeasing both the "Let's try to redeem Draco" group, and the "Let's not be friends with Draco because he's a prick and may result in conflicts with better potential friends" group (even if not giving either everything they want it is a decent middle ground).
[X] Suggest playing a game.
-[X] Dungeons and Dragons
[X] Invite him in, to join in the conversation/game, but explain you don't have room for his friends in the compartment as well.
Lastly, to the people saying there isn't enough time to teach and play D&D, the train ride is almost an entire day long (well from some time in the morning till some time after the sun sets), and this is AD&D which is rather faster to pick up than 3.X or 4th edition. And I've had people pick up and learn to play those in only a few hours (including making characters and getting started on the game) and that was without someone with a comprehensive knowledge of the system that can quickly answer any questions...
Actually...
@Halpo133 would it be possible that the D&D books would have acted as skill books for the RPG/GM skills (or whatever skill that would fall under)? As in skills for playing and running role playing games? They do after all rather extensively explain how to do those things. Or would Magic of the Multiverse trait overwrite their ability to act as such? Sure it wouldn't be a particularly useful skill so far as adventuring and such, but it would be a fun one to have and be able to grind up to the point of being an amazing GM that can quickly hook most anyone on the games we run.
owrtho
