There exists the level on which this joke is simply that Jon plans to take Liz to Chuck E. Cheese, and naturally a woman of Liz's refinement will not appreciate the child-oriented restaurant. The scenario may or may not be true, but it's why Garfield is sarcastically comparing Jon's date to A Night to Remember, the ironically-titled movie about the Titanic disaster. I've pointed out before that the kind of innocence and enthusiasm Jon displays in panel 3 is probably the reason Liz likes him. It is, naturally, the same quality Garfield frequently attacks in Jon, because he does not possess it himself.
It's dorky to take a grown woman to a kid's arcade/pizza joint (unless it's some puzzling form of slumming?), but Jon keeps doing things like this, and Liz keeps dating him. The long-term reader realizes Garfield is essentially sniping about nothing, and projecting his feelings onto Liz. One of those feelings is insecurity. Whatever, Garfield, like you don't like pizza!
In a weird reality-twisting moment, I wonder if Garfield is acknowledging a historical close-call: in the early '80s during a period when the merged (Chuck E. Cheese's) Pizza Time Theater and ShowBiz Pizza Place were struggling to unify their identity, and unable to sustain exclusive contracts with their animatronic developers, Creative Engineering, the company looked for ways to phase out the ShowBiz house robot-band, The Rock-afire Explosion. The plan was to introduce animatronic licensed characters from other media. Spider-Man was considered (?). Superman was a contender. And Garfield was in the running. Yogi Bear won. The plan failed. The Rock-afire Explosion was abandoned, the Yogis dismantled, the ShowBizzes re-converted into Chuck E. Cheese's. We missed our chance for a giant animatronic Garfield to sing doo wop while we ate crappy pizza.
Special thanks to the ShowBiz Pizza.Com archive for absolutely all the above information.