I agree with others that there should be some kind of scoring. It's surprising how addicted people get to trying to improve their score, especially if there is some leaderboard present. Just give people points for the activities you hope they will do.

You could give points for correct guesses (maybe with time limit) and give even more points for creating their own fights, possibly depending on how "good" the combination of movies is (not sure how to determine that).

When using this site, it beat my expectations in that I actually found some movies I intend to watch after using it. Stuff I had forgotten exists, like I had watched Evil Dead 3 but skipped 1 and 2. Thanks for reminding.