What is more babyish?

I don't really think Pokemon is JUST for children, it's a perfectly good game to play for a lot of ages. The age rating isn't how old average people that play the game are, the age rating is just a recommended minimum.
As for minecraft videos, my little sister that's about 9 watches similar minecrafters, and yes, I endured about 10 minutes of watching LittleKelly to get an idea.

I'm pretty sure the definitive answer is: Your 'friend' is more babyish. Either that or he's being a creep and hunting the Little Kelster down.

People like what they like.

I like JRPGs. The early Final Fantasy games and Dragon Warrior games reminded me of the old table-top Dungeons and Dragons that I played with the neighbor kids when I was younger, except the computer did all the dice rolls for you to speed the game up. So I've had a pre-existing appreciation for that type of game play.

Pokemon is just a different take on the JRPG. Instead of having a party of 6 people, which would include a Knight, Cleric, etc. you have 6 pokemon with you. It's still the similar turn-based combat, except you go head-to-head vs. 6 on many at the same time.

Just because it has a "kiddie" skin to it doesn't make it any less of a competent JRPG. So if you like that sort of thing, you like that sort of thing.

I'm 42. Started playing gen1 when it was new when I was 23 or 24, and plan on buying gen7 next month.

Playing anything related to Pokémon is childish. It was created for children. I tried the Pokémon go app....and kept asking myself, is this supposed to be fun? What is the point of all this stupid stuff? I, as an adult, found it silly and rather boring and pointless.