In the manga, Light begs Ryuk, to kill everyone in that room. So let's say, Ryuk would have killed the Japanese Task Force and the SPK. Would Ryuk die after he killed them?
1) By manipulating the death of a human that has influence over another human's life, that human's original life span can sometimes be lengthened.
2) If a god of death intentionally does the above manipulation to effectively lengthen a human's life span, the god of death will die, but even if a human does the same, the human will not die.
This seems pretty explicit to me. Note that this seems to refer to killing with the death note but if a god of death kills by any other means he is given an "Extreme Level" punishment and then is executed.
What's love got to do with it? Nothing
Doubt it. Ryuk did not love light (which is the requirement for dying). Ryuk was just hanging around for the entertainment. Even if he killed everyone in the room it was probably to extend his entertainment. He however would never do this because he was impartial to light and had explained this to him in the very beginning. Whenever he did help light it was because he didn't want to be further bothered. In this case saving light would have caused him more work.