Yep, I'd guess the seal(s) have gone (not the gasket), which is why the coolant is draining out of the hole in the picture on the bottom of the housing (which is there to stop leaking coolant getting into the engine oil and so you can visually see the internal seals have failed).

You really should remove the pump housing (both parts) and strip pump and replace the 'O' ring and the two shaft seals and refit the whole lot with fresh gaskets.

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