I've heard people say this several times, in response to a funny video they watched,
Gets me every time.
This time I see this response the person put a laughing emoticon at the end. Does it mean it makes them laugh every time?
The phrase means that whatever it is engenders some strong emotion: here it will be laughter, but in other contexts it might be tears, surprise, or embarrassment.
"(something) gets me" is a catch phrase, everytime is an intensifier that suggests 'I can never get used to it'.
Eric Partridge in A Dictionary of Catch Phrases explains that gets me!
Loosely applied, the phrase could also mean never fails to amuse me or such.