Can I play video games even if I have a hyphema?

I would not. Follow your ophthalmologist's instructions for treatment of you hyphema.
Not really.. There is a significant risk of rebleeding in hyphema which increases risk of glaucoma and a variety of other complications. For fastest recovery we ask patients to minimize ocular motion. We will also put patients on drops that prevent the pupil from moving internally to cause bleeding. Of course, follow directions of your treating doctor, but until then and probably after, avoid video games.
Better not. Hyphema (blood in the anterior chamber of the eye typically caused by injury) resolves more quickly with fewer long term side effects if the blood settles in the eye quickly. Visual (and activity like work, reading and exercise) is best curtailed until the blood is gone. The doctor may dilate the pupil to help avoid rebleeding. Watching tv may be ok since the eye remains relatively still.