(Poor hitter 2 needs some help with the crowd):
Isn't hitter 2 more likely to actually drive in one or more runs per game? Plus, he is always in scoring position at least once per game.
No, he won't drive in more runs (well, technically he won't advance more baserunners extra bases, which is where the long run value comes from).
If the baserunners are distributed randomly for both, the singles hitter is going to be getting hits with runners on 3rd twice as often as the doubles hitter will, and will drive in more runners because of that.
He'll also get twice as many hits with runners on 2nd, and drive in at least as many of those as the doubles hitter (chance of scoring from 2nd on a single is close to 60%).
Runners do go 1st to third about half as often as the score from 1st on a 2B, but that's balanced by the fact that our singles hitter is getting hits twice as often still. If my math is right net expected bases on 2 1st base runners for our singles hitter is 2.56, and net expected bases is for our doubles hitter on his 2B with a runner on 1st is 2.38. Our singles hitter won't drive anyone in this way, but following hitters will have far more opportunities with runners in scoring position than they will after the doubles hitter.
All that ignores the costs of the GIDP and Ks in the original hypothetical, but there's a runs created formula you can plug all this into, and you'll find that the expectation is still substantially higher for the singles hitter even given the unsubstainably high GIDP rate hypothesized.