I'll explain the words in inverted commas first, and then put the original sentence in to simpler ones which have a similar meaning.
If something is "mystic", then it could be strange, and usually has something to do with magic.
If something is "intensifying", then it is getting stronger.
"Perception" is the way something is seen.
"Entrance" is entering, or going in to something, but could also be the place of entry.
So, the words in inverted commas could be said as "like a strange increase in strength of the way he saw things, rather than any changeful entry into another world."