in the third round there's actually supposed to be some sort of ending sequence with RETRY/QUIT options, so dying in the third round isn't supposed to close the game (un)fortunately
The only thing you’ll see is a shot in the face from which you will never recover. It’s the ending. Pathetic, but fair and believable.
Closing the game because there’s essentially no point in continuing to keep it running is quite natural. Especially given the almost complete abandonment of the UI, pause menu and other stuff.