Anytime you deal with a fridge you are going to need a lot of battery. Your case does not seem unusual.
Using a dual battery setup is not absolutely necessary, but fridges are the reason you see that topic frequently discussed on this board. Multiple batteries start to become mandatory if you plan to power the fridge for longer than a single overnight without running the vehicle long enough to help recharge things, and/or do not have an alternate charging method like solar to assist. (Even then solar keeping up with a fridge can be difficult to pull off.)
I have a small (Indel B TB18) fridge and get by with a single starting/house battery, but it is a Group 31 with 100Ah capacity. In it's final months even it stopped being able to last the night and I had to buy a new one recently.
As plh calculated for you it seems you don't have quite enough battery to comfortably last that long, you are on the edge of the limit. When you run a fridge, the actual fridge is only half the expense and consideration in the install. I easily spent 1.5 to 2X what the fridge cost on the supporting infrastructure behind it, namely a big, high amp hour battery and I had to install heavier gauge wiring and connectors to get suitable power to it's location without incurring voltage drop with further exacerbates keeping the fridge online. Fridges are like a whole thought out install thing, not a drop in add on. But there are multiple ways to go about handling it.
Since I do take my chances with a single battery setup, I always have a Lithium jump pack on standby, and not a wimpy one either. However, the safety cutoff on my fridge has proven to leave me enough to go ahead and start the engine. It's not happy about it but it will do it. (This was when my battery was nearing the end of it's life and was starting to not hold it's own overnight and into the following day.)
You can probably make your setup work a while for the meantime, but you'll likely need to be getting that engine started first thing in the morning.
Right but one would expect the duty cycle on the compressor to be much lower that 100%.
He's also likely assuming your battery is healthy and actually capable of 60Ah. When figuring stuff like this, always calculate for the worst case scenario. Assume it is going to run 100%, what if it's a warm night? Pad the numbers against you and if you can pass that with a safety margin, it might work smooth for a time. This is not a area where good enough gets by. You need a little more than enough and then maybe, just maybe, it might not give you grief.