Yes, as they can no longer complete the current turn. Traditionally chess is played with time limits, so it makes sense that death causes the current turn, and only the current turn, player to lose.
I propose the alternative that death is instant disqualification regardless of game state, which incentivises murder as a strategy and adds an additional psychological tax but also a necessity to resolve disputes in a way that really makes the Han/Greedo distinction an important one and would make for a fun "spaghetti western involving but not necessarily for intellectuals" flick.
For practical purposes this is not correct though. It would be trivial for the person whose turn it is to make _any_ legal move to shift the current turn over to their now-deceased opponent and as such win the game.
This is logical, but the situation when the other player dies needs some solution too. Because the living player finishes their turn and then ... what? There isn't even anyone to have a turn anymore.
So for the sake of completeness, I would expect the rule to cover all deaths at the table.