Hi warren, nice to see you again.
Yes, GSAP can handle animation in a game, but there is a lot more to making a game than just making things move.
For character movement TweenLite may not be the best choice as a tween has fixed duration and destination.
For instance if pressing the right arrow key creates a tween that moves something 100px to the right of its current location for 1 second, what if the user wants to move 300px? will the user need to press 3 times or will you have to program some awkward logic that repeatedly checks if a new motion tween should be created once the first tween ends. What if while the character is moving to the right the user hits the down arrow? Will you need to write code that kills the tween that is moving to the right?
Character movement is usually handled by making small increments to x/y values while a particular key is down.
If you want to move enemy ships around or fire bullets, tweens would be great.
My suggestion is to start small with very very low expectations. Get something small working and then try to figure out how to add more features.
95% of building your game will be writing code un-related to animation: collision detection, scoring, generating enemies, generating missiles, programming input controls, etc.
I would suggest going to some sites that focus on general HTML5 Game Development and learn the basics without using GSAP at all. Add GSAP only where it makes sense or makes things easier.