I got the "playing videogames won't get you a job" talk (funny how that worked out), but as far as working in the industry, I'm sure I'd have their support. I remember making drawings and having little ideas for games. They were pretty supportive of that. My father even helped me write a letter and mail it to Sega about an idea I had for a game (IIRC, I think it was just a Sonic clone lol).
So when college came around, I got into Computer Science because I've been wanting to make games since I was a kid. There wasn't a direct game design curriculum at the school I went to at the time, but I figured Computer Science was kind of something I could apply to all facets of development, so I went with that. By the time a game design course was created, I was already in my final semester.
In the end, I'm not in the gaming industry, but I think if there was a curriculum at the time that directly involved games, they would be fully supportive. My folks never tried to push me toward any particular field.