I agree that is too small for a betta, and it also encourages keeping the betta without heat in potentially chilly environments, but it is a fun concept. They sure did well with their funding goal.
Beneficial bacteria are important no matter how large your water changes are. They quickly process the highly toxic ammonia that fish are constantly producing. Most of the nitrifying bacteria that live on gravel and filter media occur as a biofilm that is stuck to the surfaces. Since they are not free-floating, I wouldn't expect a strong flushing like that to affect them much.