Stroller is the word you were looking for for baby cart. I hate when I can't think of a word, it pisses me off until I look it up or somehow remember and I can't focus on anything else.
I've seen these sorts of things at subway exits/entrances in airports, where you have carts for moving lots of bags at once. There might also be shops nearby with shopping carts that people have tried to take on the escalator in the past.
I'm not Korean(perhaps someone familiar with the place might be able to offer more insight), just offering some possibilities, but it's difficult to know without more context.
I was about to say, they put a giant pole in the middle, no one who is fat will enjoy fitting through that and some even fatter people will never fit lmao