It is perfectly normal to avoid dating someone who plays videogames as a primary hobby

I spent many years as a gamer (maxed combat in RuneScape, 500-person clan owner)

It is perfectly reasonable to avoid dating someone who plays videogames as a primary hobby (especially a multiplayer game) for the following reasons:

  1. You can't pause every kind of game: If you are someone who participates in 'raids' on a multiplayer game, you cannot pause it. The entire team may die.
  2. Loose social connections: Most of the friends that you make on a videogame are temporary, even if you play with them for years. I have tons of 'memories' with pixels representing real people I will never meet.
  3. Lack of physical activity: Most gaming is sedentary. For us white collar workers, that's adding more 'sedentary' to our already sedentary lives. Health wise, most of us cannot afford this. You will inevitably gain weight unless you are monitoring calorie intake.
  4. If it's not multiplayer, it's essentially a solo activity: If you're going kayaking or hiking, you can do it as a couple or with friends. Unless it's a multiplayer game, you can't involve a friend or partner. Most people don't want to sit there and watch you play a game.
  5. There isn't enough 'positive output': If your hobby is the gym, you're walking away with improvements to your health and physique. If your hobby is diving, you're forced to make friends (never dive alone). If your hobby is reading, you're increasing vocabulary and exercising your brain or learning new information. Gaming doesn't produce enough 'positive output' for your life.
  6. Time sink culture: Most videogames are now a grindfest, designed to reap the maximum amount of hours from your life so you feel like you 'got your money's worth.' Have you ever been running on the treadmill in The Sims and realized you should be running in real life?

If someone doesn't want to date you because gaming is your primary hobby, it is completely valid and reasonable.