I have it too. But mine is about twice the length of yours. Sometimes can be seen venturing out of its rock to forage. It's just a polychaet worm. Nothing to be worried about. As far as I know they don't hunt fish but will scavenge instead. They have no apparatus to capture prey effectively. So far all my gobies are unharmed..even my pipefish. Just leave it in there and enjoy the monster.
Btw..have not heard of tamil tiger gobies...can give the scientific name? Is it Stonogobiops sp. ?