Minna Atsumare! Falcom Gakuen

Both incorporate - many game references - gaming eastereggs - and jokes about said games Falcom Gakuen is absurd slapstic comedy about Falcom games (Ys, Legend of Heroes, Xanadu) in a fictional world, Hi Score Girl is taking place in a realistic 80s setting but has a lot of direct and well informed game related humor (Street Fighter, Double Dragon, Final Fight... and tons more). If you're into Japanese games, especially in the retro territory, both are very recommendable. 

characters from different franchises are put into a school setting 

Both are flash animated comedies. Both are setted in RPG like world and both have short episodes. Both have school setting where game characters go to some kind off academy. Both anime have very similar feeling, if you liked one, you´ll probably like the other one. 

Do you like RPG themed slapstick anime? Then these series are for you! From having great and funny characters to hilarious jokes and settings. If you want to have a quick laugh make sure to give these series a watch and I'll guarantee you that you won't regret it. 

Anime shorts. Using characters from popular series. One involves Falcom video game series such as Y's, Trails of the sky etc. The other one is an alternative setting of the Lodoss series/movies/OVA. Both series are not the true portray of the characters. More on the comedy side.