It's the kind of funny that makes you almost laugh out loud, but it's more smart and a fun process. It's like the really smart meme kind of funny. I would compare it to a fake sneeze because it's an almost laugh, but a lot more fun.

"Dry humor" maybe, for the style?

Did some searching and one term that came up was the German word "Schmunzeln" which I hadn't heard of before.

wiktionary describes it as:

to smile slightly, smirk (not smugly, but in an amused or contented way; e.g. when witnessing an amusing scene or conversation)

Not sure if that's quite right or not, but might be what you're looking for if you want a word to describe the reaction? (Maybe someone who actually speaks German can confirm...)

Amusement? That's when it's funny inside, but you don't let the laugh out

Of course, there's a German word for it, lol. I think Schmunzeln is closest, but as you said, in a dry humor kind of why. Dry humor is really, really close, but not quite perfect.