I've just checked with Seriously Fish for Brachygobius doriae as I knew next to nothing about them. It does say there are a few different species of bumblebee goby so your son's fish might not be B doriae.
According to SF, your son's fish would appear to be behaving like a breeding male - colour change, guarding a cave etc.
When in spawning condition males take on an overall reddish tinge with the dark bars on the body becoming paler, while the first yellow bar in females becomes brighter.
An individual male will select a site and display to female in the vicinity until he finds a receptive partner. Around 100-200 eggs are deposited in the cave after which the female departs, leaving the male to guard and tend the clutch.
It also says they prefer quite hard water, from 143 to 357ppm, so your hard water should not have been a problem for breeding. Some sources even say that these fish are brackish water fish, though others say they can be acclimatised to freshwater.
I don't know what to suggest. Are the puffers and otos all OK? No signs of sickness or being picked on by the goby? If it's just the gobies that suffered, that does suggest the male wanted them all out of the way. After a year, it shouldn't have been lack of salt in the tank; they would surely have succumbed to that before now if it had been a problem.
But one thing most sites are clear on - if you want the fry to survive, they must not be in the same tank as other fish. They suggest moving the cave, complete with father, to another tank filled with the same water (bumble bee gobies don't like water parameter changes). SF gives incubation time as 7 to 9 days so you'll need to do something soon if you want to save the fry - which might be an option for restocking the tank with gobies.