That video is again on the beta, while it would be interesting to see the same test on the current game, a few fps don't really matter to me.
I've played PC games back in the day, playing a game at 20fps with dips to 10 fps was affecting my performance in first person shooters.
I would love to see an alien test the PS4 vs PS4 Pro to see if there is any difference in lap time, however aliens tend to run alone at the front, so they wouldn't have enough cars on screen to cause an fps drop.
If you are running at the back or mid pack, then .7 .8 would be cheaper gained through practice.
If you are running a PS4, here is a test - set a time in a custom race, start at the back and have the AI drive faster cars, so you never catch up, but are not benefiting from their slip stream. Once you have set your fastest time, go into arcade mode and run the same car track and see how much you can beat your time by. Obviously you will be improving each time, so go back to the custom race and beat it again.
I suspect it's more likely that your driving inconsistency is more of a factor than the games fps, unless you are an alien or very close to one.