Meoshi leaving his handheld game system with Saki in his bad ending isn't just a token of his for her to hang onto, it's symbolic on two different levels:
Portable game systems are designed to be, well, portable - consoles that you can take with you in order to play games while you're somewhere other than your home. Giving away his handheld indicates that he's given up any hope of conquering his anxieties and has resigned himself to being a Hikikomori: he doesn't need a portable game system if he never leaves the house.note There are other reasons a die-hard gamer would have a handheld, such as games only released for that console and the ability to game in any room of the house, but bear with me, we're talking symbolism, here.
By wiping his save files and resetting all of the data, he undoes all of the progress he's made in the game up to that point and gives up on any chance of beating the game - just as, by withdrawing back into being a shut-in and cutting off contact with Saki, he's undoing any emotional progress he made during the events at the theme park and, once again, giving up the fight and resigning himself to being a shut-in.
