Who is to blame for the death of Odysseus's men at the hands of the Cyclops? Why?

The cyclops. Xenia is the ancient Greek concept of hospitality, the generosity and courtesy shown to those who are far from home and/or associates of the person bestowing guest-friendship. The Greek god Zeus is sometimes called Zeus Xenios in his role as a protector of guests. He thus embodied the religious obligation to be hospitable to travelers. The cyclops Polyphemus showed lack of xenia, despite Odysseus reminding him of it, and refused to honor the travelers' requests, instead eating some of Odysseus' men.

I'm pretty sure that the cyclops killed them. Wouldn't that make their deaths his fault?

The person who made up the story.
Because it makes for a dramatic story.

BONUS ANSWER:
In the book "A Mythical Bestiary", the author points out that when large skulls were found, it was naturally assumed they were the skulls of giants. And there was what LOOKED LIKE a single large eye socket.

But, it was the skull of a mastodon, with a large NASAL CAVITY where the trunk connected.
The eye sockets were tiny, and way over on the sides.

David