Game designer here. I'd say there are degrees in these. Most game designers I know love to play game, but which type of game that they love? Well train designer should be able to design anything, you might say that, but most people have a thing that they keen more than the other thing.

So, they may be very well verse on some genre and might not so much on some. Now, getting a job in the right company that making the right game that you are keen of might not be that easy.

I've seen some young to old designers who only play certain type of games and be clueless on other type and some who can adapt their design skills to many types of games.

But game development can't be without testing if they design something wrong, it should show up on test...

Still, sometimes you got the best devs and the test results came out surprised you.

It's easy to point what is wrong looking from the end product pov but when the design starts with a clean drawing board it's also very easy to miss things.

Game dev is hard man...