Meaning of the word "gets" in this context

This month’s article comes from Cabinet Magazine and is rather peculiar — it elevates the discussion of something my 2-year old “gets” to the rarefied realm of academic prose.The article is about tickling — why we do it, and how it relates to the very essence of humor

What is the meaning of gets in the above para?

This meaning follows that of MW's 11b

get

11 d: understand

He got the joke

The writer is saying that the 2-year old understands what tickling is. But, the discussion that will follow this paragraph takes a more scientific view of tickling.

The writer probably chose this simple way of say "understand" to contrast it with the complicated description after it of the "rarefied realm of academic prose". This difference in writing style shows a transition from the simple to the complex. This is also what the article is doing with the topic - taking something "simple" like tickling and analyzing it in a more complex way.

In this context, I would say gets means knows or understands. The paragraph you mentioned is saying that the discussion is about / starts from something a 2 year old would understand and intensifies into something more literary (academic prose). As evidenced in this link get can have the meaning of "get hold of", which means "to understand something". This is the case in the context you posted.