A bit more, Fred is correct from the point of view of an outside vent...but...
The answer being already no you do not need to vent it outside I would like to add...
This does not mean you do not need to vent it.
The rule is you cannot throw heat in to small a space and expect the refrigeration unit not to get constipation of effort.
When asked to do this by an owner I create a space above the refrigerator
so the heat removed from inside the box to outside the box can rise inside the cabinet and thru the natural process of convection gently exhaust over the space near the top of the refrigerator
Exhaust is not the only trap remember
a path for cooler air needs to be established so as the rear coils heat up the cooler air enters the rear of the refrigerator
heat transfer coils and gently exhausts, a 3/4 gap beneath the refrigerator will suffice as an cool air supply with a 1" gap on top of it being adequate too as a warm air exhaust. Remember breath in and out for refrigerators too. The heat can be useful inside a small trailer and will not amount to much camping. But throw that heat into a closed tightly sealed cabinet space and the marshmallows will go bad and the chocolates melt before the refrigerator compressor current overload shuts it down to protect the compressor rather than the thermostat inside the box shutting it off when cold enough.
The literature sold with the refrigerator gives a warning to this effect.
Hope this helps deepens the discussion a little, the afore mentioned advice is correct, unless the trailer interior is ungodly hot (like parked in Phoenix Arizona all day closed up tight)
the issue will not require outside venting.
Happy Camping, Safe Trails.