An interesting consequence (since there are only finitely many digits) is that, in this sense, almost all numbers contain every digit—a phrasing that, I think, makes the statement less surprising.
Contain -any series of digits-
Also, almost all numbers contain any given finite sequence of digits.
Did you intuitively understand that prior to watching the video?
I can't speak for him, but I haven't watched the video and this all seems extremely obvious to me.