what makes a board game designer

I'd say you are a "board game designer" when, at the very least, you have actually made a tangible and playable prototype and have played it with other people.

The distinction between a professional and amateur board game designer is whether you are doing it for a living, or not (any money you make is just a bonus).

My 2 cents on calling oneself a "game designer":

If you engage in an activity - any activity - to a reasonable extent on a regular or semi-regular basis, it's fair to label yourself as a member of that group. For example, I used to rock-climb, but I haven't for a while. I used to call myself a rock climber, but now I'd have to call myself a lapsed rock climber.

If you engage in an activity for fun and are not paid to do it, it's appropriate to call yourself a "hobbyist" or "recreational" member of that category. Continuing the above example: I was a recreational rock climber. I was never paid or otherwise compensated to rock climb.

If you engage in an activity for fun, but occasionally make money at it or have been recognized once or twice as an authority in that area, it's appropriate to call yourself "semi-professional." For example, I ran a PnP website for 10 years, had games published on other websites and in books, did paid game design work for several companies, have had two games licensed and published, self-published another game, have spoken at several conventions, and run Protospiel South. I consider myself a semi-professional game designer.

If you engage in an activity and it is your primary source of income, it's appropriate to call yourself a "professional" member of that category. Continuing the above example: I was employed by Steve Jackson Games for a period of time as a Game Developer. During that time, I was a professional game developer. At another time, I was employed to design educational games for students in grade school. During that time, I was a professional educational game designer.

All of this is a little like splitting hairs, though. What you want to label yourself as is up to you, and what you think of as one thing, I may very well think of as another. What's described above is simply the way I choose to look at the world. Your mileage may vary. Nonetheless, I hope this helps you set up a framework that works for you.

I think if you've made a game that other people play you're a game designer, as you've designed a game.

As long as you continue to make games for other people to play, you continue to be a game designer.

Once you've stopped, you are no longer a game designer, you've just designed some games. You *were* a game designer.

If you sell a game, or get paid for it - you're a professional game designer. Otherwise you're an amateur game designer. I personally don't think of either of those as better than the other - just different in focus.

If you've designed a game that went to print, and sold enough games to make a profit - then I'd say you're a successful game designer.