Oh boy. I’m gett’n 'nam flashbacks over here. Though it was less a “fight” and more a “there is too much to teach” from my school, but I digress.
I am interpreting “generic ‘game design’ direction” as the school teaching generalist skills. That means things like 3d Modeling, Animation, and how to use an engine such as Unity or Unreal. Or, maybe I’m wrong, and it’s more theory. Design and Concepting. Learning how to talk to the player with out expressly telling with words.
Whatever it may be, here is something I would have liked to have known when I was in school; you are learning VFX. I know, shocking right. How can this be VFX? Nothing is blowing up! 
Every. Single. One… of those skills is useful to have, some more indirectly than directly. You literally can’t know too much. So where do you start? That’s a question of the ages right there. In a way, you have already have. You’ve posted here. At this point there is three… almost four years worth of VFX banter archived here. I didn’t have this when I was in school… blah blah blah, get off my lawn. 
I’m sure you’ll find something to break with the know how exhibited here. Just… focus on your studies first. If you don’t have a solid basics foundation, you’re going to hurt yourself. Pacing is a thing.
Everything you mentioned (“Unreal, Houdini, and After Effects”) is very much worth knowing, and I’m probably understating that. But unless you are learning these at your school, I must warn to be careful to not overbear yourself with extra work, especially with Houdini. Houdini alone is at least a semesters worth of stuff if you’re coming in straight new to it.
With that said, here is my suggestion on what you can focus on while you are in school, that more and more is a universal VFX thing to know. Learn shaders. If you can code, that would be best, but if you can do it with nodes, that’s great too. As far as I know, generally, no one cares how; Can you make or not?
It’s a results profession. Studios may very. Batteries not included.
I’m going to direct you to this thread, as I feel it will be helpful. It’s something you wouldn’t know to look for unless you already knew to look for it. A sort of Isla de Muerta post.
As for everything else, start searching. 
Good luck on your educational travels!