Not a comics fan?
The character in the first screenshot on page 2 is not the Caped Crusader, who is Batman. It's Bat-Mite, an Imp from the same dimension as Mr Mxyzptlk who idolises Batman and dresses up as him to fight crime.
I'm quite surprised that Bat-Mite appears in the game, even if it is heavily influenced by the West-era comics. He was very much a product of that era where Batman got silly for a while, and had hardly appeared for 15 years before he was all but completely retconned out of existence during the Crisis on Infinite Earths in 1985. (Which is why I don't blame you for not recognising him.)