"I swim every day."
The video you linked is very complete, but I personally think that the difference goes like this:
「毎日泳ぎます」"(It's certain that) I swim every day".
「毎日泳いでいます」"I have been swimming every day".
Where the first one is more of a statement about a routine, while the second case focuses more on the repeated action that happens every day as a routine.
Both are correct, but I think a Japanese person would normally use the first one for this verb in particular. Things like explicit routines like work or study might prefer the ～ている in some cases.