Dragon Roost Island is not Death Mountain for starters. Apparently it's Zora's Domain. IIRC the 'actual' Death Mountain is that volcano where you got the iron boots though that may not be true and I don't remember where I heard that from. Anyways, Goron's survivability isn't really dealt with. Most likely they either evacuated due to travel across the ocean being very impractical for a stone monster meaning the great ocean was just a terrible place for them or they mostly died out and/or went underground for the same reasons. No matter the reason their traveling across the ocean surface would be exceedingly difficult due to their immense weight/density so they wouldn't be all that common up top.
It's also possible that they're simply stuck down in old Hyrule and frozen in time down there and the ones we see were the lucky ones who were away at the time.
However, the real 'most likely' answer is that the Gorons were planned to inhabit one of the two cut dungeons. Had said dungeon not been cut we likely would have seen a volcanic island full of gorons or their descendants. When said dungeon got cut, however, the majority of gorons went with them and the few we see in the overworld are simply the ones that remain. This is especially true since evidence points to the Goron Mines in TP being one of the two cut dungeons.