I have a similar 15-amp charger on my boat, and it has never had a problem keeping up with the fridge and a couple of lesser loads: an alarm system and a few led lights, as well as the all-important bilge pumps.
I believe my fridge draws about 7 amps when it runs, which is not all the time.
You might need more if you run a lot of lights at the dock, or other loads. But even a heavy load (12 V hair dryer) won't kill the battery and the charger can catch up.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida