As opposed to the less lethal explosions of smaller stars, which are good for quick tans.

If a star explodes and its system that has no life, is it "deadly"?

Stringently, yes. To be "deadly" simply requires something to possess the ability to cause death. Actually causing death isn't a requirement.

(Non-exploding stars are plenty deadly, too.)

Except if the exploding star has no life anywhere near it, it has no ability to cause any actual death. I don't disagree that if something were (hypothetically) living in its blast radius, it would be killed, just that if nothing (hypothetically) were so living, it can't really be capable of killing said hypothetically non-existing things.