Nobody has said that the GoPro is terrible the question is what will I be disappointed at.
Underwater video is a matter of skill and that night dive video you show is not really the best way to compare, however even in that case the gopro shows plenty of clipped highlight and blurred corners, the dynamic range just is not there because the sensor is smaller so it is true that there is a difference in price but it is also true that it shows to be honest. If you want to see what the RX100 can or not do is probably better to have a look at my night dive clip, majority of what is in there could not even be shot with a gopro as it is close range work.
The gopro is best suited for wide-angle ambient light shots to modest depths, as you go deeper the lack of custom white balance and the poor performance in low light shows the limits pretty soon. There are example clips on this thread of gopro with two sola light 1200 to shoot some daylight wide angle that could be achieved normally with a camera with custom white balance which would be actually cheaper than a gopro and two solas. Because the gopro does not have custom WB the already poor low light performance is made even worse by the fact that the filter absorbs light, so if with a normal compact you can push a filter at 20 meters and still looks good with a gopro it looks green and you need lights.
There are plenty of choices out there and the gopro is the choice as a start up kit, but you don't need to spend $2000+ to make an improvement.
A compact camera like a canon sx260 or a panasonic tz30 that can take macro costs you $1200-1400 including a focus light for close range work that with that set up you can do but you can't with a gopro
My sony rig costs over $3000 and so does my panasonic rig but the difference shows as you can see in mine and other videos, I have not had the chance to take any of my rigs into shallow water but I am pretty sure that the image quality will show. It also has to be noted that majority of 24mm compact camera only need a dome not a full wide lens to produce decent footage and because the CAN WB there is no need to be that close or have lights.
There are plenty of choices in the market but people don't know it because camera manufacturers also produce camcorders and do not to cannibalize their own market share so let the action camera people chip in
It is great that gopro exist to push the envelope no issues with that I recommend the camera myself to beginners in video but I make it clear that it cannot do macro and it really only good for blue water ambient light shots preferably above 18 meters, when someone then has pushed this to the limits and is thinking of spending $1500 on video light for a gopro I usually tell them to change set up because they can capture different types of scenes and behaviour that even with lights are not a possibility with an action camera today. It is of course entirely possible to spend money on lighting but then you really come to the point where you realize you need a different camera so you can keep the lights and then spend some more money on a better camera
To make it clear I love the gopro is a great little camera that I would give to my son to play in water but having the money I would not bother taking in water myself, one day when I will live close to a warm sea I will take all my rigs in water on the same dive for a true comparison!