The video makes a valid point. The "present perfect" word pattern is the one we use to describe our experiences. For example, I could list
"I have gone to France"
"I have had the measles"
"I have danced the cha-cha"
as experiences I have had. What unites these examples has nothing to do with the times when the events occurred (whether they be recent, long ago, or continuing into the present matters not). What unites them is that they are all experiences that I have.
When you tell me that you are doing something for the "first time", you are announcing to me that it is an experience ("the first time doing it") so the present perfect word pattern is the one to use.
There are ways to express the same idea without using present perfect:
a) "This is my first time seeing this"
b) "This is my first time for seeing this"
c) "This is my first time to see this"
Why are these OK? Why is the present perfect not needed here? It is because in each case, the sentence is really just "This is my first time", which is a perfectly good sentence. The additional phrases ("seeing this", "for seeing this", "to see this") contain no active verb. They are just subordinate clauses.
For example, "to see this" is a noun clause so (c) is just like the sentence "This is my first time swimming". In (a), "seeing this" is an adverbial clause modifying "first" so it is just like the sentence "This is my first time here".