Depends on who you ask and I'm no expert or jewish but I'll go on limb and say that observant Jews probably consider playing video games as going against the spirit and purpose of sabbath since most conceptions of work (melakhot) involve operating devices in some form, though how many violations are incurred when using a computer on sabbath is probably somewhat contentious. Whether using electricity counts as igniting a fire or not is a topic of debate, but also playing games may involve additional prohibitions such as recording.

Here's some relevant wikerpedia

I also found some questions from obvious children protesting the restriction of video games during sabbath on similar grounds to yours when googling this, which I thought was funny.

As for me, my religion is video games.