I like to game in the evenings for 3-4 hours straight and afterwards my eyes are completely dry and red. I have the same problem during the day at the office on my PC too. I've been told to get a tear film test done at the eye doctor, but I'm not sure if that's really necessary or if there are just simple tips that could help.
Don't stare at the screen non-stop without breaks - take a short break every half hour, look out the window or at something far away on your phone. Artificial tears help right away, and humid air in your room does too (a humidifier or just let some water evaporate), and make sure you actually blink while gaming - a lot of people completely forget to do that. If it doesn't get better over a few weeks, it's worth getting it checked out, but try the standard tricks first.
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