Perhaps this model TrippLite isn’t up to the task, as you surmise…is it not an Isobar series?
You might be safe enough to run the HD cable box coax directly to the monitor esp. if you live in a subdivision where the utilities are undergounded, and/or you can verify that the cable co. has attached their feed to your residence ground at the service entrance.
But if you want specific surge protection on the coax (a good idea in most cases where electrical storm activity is prevalent, and there's overhead pole wiring) you might:
1. Upgrade the surge protector to say Panamax MAX 8 Coax at $49
Here a unit specifically designed for cable coax pass-thru.
2. Keep the TrippLite and instead run the cable coax thru an inline protector, perhaps a silicon diode type. I don’t have a link at hand.
bill