Filling electrical/electronic components with oil is commonplace. The general reason is that the oil is not compressible and thus there is no reason for a heavy metal case to resist the pressure. In this particular case, it also allows communication of the ambient pressure through the case, and the diaphragm you see re-installed, so the pressure can be accurately sensed. Tracking pressure changes and time is the basic function of this device.
It should be noted that working accurately and reliably is essential to the divers health and life. Some types of diving absolutely require this reliability and others, less so. A diver may be making critical decompression decisions in relation to his or her remaining air supply. Without the computer, they simply can't return to the surface without guessing what should be accurately tracked and computed.
Once the work shown in the video is completed, the computer should be put in a pressure test chamber. Many dive shops have them. There it should be put through it's range of pressures, compared to a known good pressure measure, and then through a range of pressures as though for typical dives, to verify that the instrument works as it should. Actually measuring pressure and assuring the thing does not fail under pressure MUST be done. The diver can decide if they want to trust the thing based on this testing.
FYI - I am a retired dive instructor trainer as well as someone who has worked professionally with electronics.