No run...but technically not a force out.
By the rule book definition of a "force out", you can only have a force out against a runner who is already on base and is forced to advance by the batter becoming a batter-runner. So the definition cannot apply to a batter running to first base.
There is a separate rule for that. If you read the rule about a run not scoring if the third out is a force out, right next to that is another rule that says no run scores if the third out is made by the batter before safely reaching first base. This covers all of the possible ways a batter can be put out- strike out, fly ball out, or committing an act of interference, for example.
So, yeah, it looks like a force out, because most force outs are executed by a fielder touching the base while holding the ball. If you call it a force out, everybody will probably know what you're talking about, and the end result will still be the same. But it's not really a force out, not by the strict definition in the rule book. No run scores here because the batter did not safely reach first base.