When the speaker likes something with insane enthusiasm but can't think of a reason why. The feeling is usually very specific, intense, and difficult to put into normal words.
(The wording isn't supposed to be mocking autistic people, the experience itself is just widely associated with autism. Just don't use this word to be a dick)
"why do you constantly use this sound effect when editing your videos"
"i autistically like it, it'sjust unexplainable i find it cool as rocks"