The 4s esc should be more than capable its the motor that pulls it along so as long as the esc can more than handle the power the motor will draw then should be fine.
I've got that esc as I'm only using 4s not had a chance to test properly yet still finishing mine but it seems to be a popular choice so not heard of any problems as long as you match it to the right motor and don't put lipos above 4s in.
With regards to the video I'm not too sure 13t pinion seems quite low but I've not had a lot of experience with gearing so I could be wrong, but although it might look fast you don't know what his temps are so could look fast but he might be cooking something there, but again I'm not an expert so could be wrong.
I would do a bit of research on this forum,have a search on here regarding the gearing and maybe start on 19t and see how you find it then maybe experiment from there if you want different speeds,but keep an eye on temps .