What year and how many hours do you have on the machine. According to the specalog for the machine from Cat, the swing gear box holds 1.5 liters of oil. That is about a quart and a half.
In my experience with swing gear boxes, they are all planetary units with very little room and no provision for cooling the oil. The oil will get warm and expand. The other issue is when filling the oil, it takes a lot of time for it to drain into the box and fill while expelling all the air caught under and around all that gearing. Draining and refilling the box takes time. The common issue while refilling is air burping up through the fill tube and making a mess. Then people pull the dipstick and assume it is full when it isn't. The other mistake is putting too much oil in the box figuring it will drop down some as it is used, and the box now expels the excess through the dipstick or the breather if it has one. Another issue happening on some machines is that the bottom bearing in the swing gear box may be lubed with grease and not the oil in the swing gear box. An operation and maintenance manual would let you know if that is the case in your machine.
A continuous flow of oil out of the breather or dipstick tube would indicate a leaking seal in the hydraulic motor which would force hydraulic oil into the swing gear box. It was mentioned above about the possibility of a case drain filter being plugged. No manufacturer that I have dealt with puts a case drain filter on the hydraulic motors. Cat puts a case drain filter on the hydraulic pumps. All case drains for the motors on machines that I have dealt with go to the machine return filters or the directly back to the tank.
Swing motors can be subject to very high pressures when the house is turning and then the control is moved to stop the turning. There are provisions in the motor to handle and vent that high pressure so that it doesn't damage the motor. A blown seal may be the result of a problem in that area of the motor. The motor itself may also have internal leakage on the seal plates or piston and barrel assembly that may cause high pressure in the motor case. If your motor is leaking into the gear box I would suggest a call to your local dealer asking if there are updates to that motor before going any farther. You might be able to unbolt and lift the motor out of the mount on the gear case and then use the machine hydraulics to turn the motor shaft and watch for a leak. Keep in mind though that with no load on the motor, it isn't likely to show a leak from the shaft.