This could get really popular since people loves playing games and breaking records. But the thing is, is this really be considered gambling? As far as I know this one is just a contest unless the player stakes something to have a chance of breaking the record. If somehow some gambling platform implements this kind of promotion/challenge, and implements an entrance fee to participate in breaking the world records of certain game speed runs, I believe even those people who don't usually participate in this event will be attracted due to the possible winning a huge amount of money.
If the speed-runner is the same person who happens to have a wager on whether he will be able to break some record or not, then it would not be gambling, as the result of the game would completely depend on the skill of the speed-runner to break his record or the record of other speed-runners. Though, the gambling part would be to have other people (who do not have anything to do with speedrunning) to have a wager on whether any particular player would be able to break a record or not or whether that player would be able to reach some time-mark in their next run or not. That is legitimate betting on something which is very similar to a e-sport, though, the competitiveness within the established e-sports like Dota and League of legends is more obvious than having different speed-runners to battle for a world record.