"Life" means splitting hairs finer and finer. Are bacteria alive? Viruses? Prions? The distinction is ultimately meaningless.
Generally viruses and prions are not considered alive as they are not (theoretically) capable of self replication.
Viruses don't have any of the mechanisms required for self replication - they only reproduce if a different organism is coerced into duplicating the virus's genetic material. Specifically the virus genetic material gains precedence over the cell's own material once the cell dissolves the protein shell.
Prions are literally misfolded proteins - saying they're alive is not different from saying any arbitrary polymer is alive - plenty of polymerization processes essentially have the same construction behaviour: rely on the bond affinities to morph neighboring identical molecules into identical construction.
Other molecules alter the shape of proteins not like themselves, in otherwise similar ways. We don't call them alive, either. Prions are interesting in that their action produces more identical action, in an exponentially growing fashion, unlike other, otherwise similar, processes.
If you like, you could say the prion's shape, itself, reproduces, given a substrate of conformable prionic proteins. That makes it more like a meme.
However, arguing over this terminology is irrelevant.
I wonder whether anyone has measured temperature reduction in a runaway prion replication process.
Richard Dawkins has written an excellent essay on this matter (the human desire for absolute categories):
The tyranny of the discontinuous mind
https://www.newstatesman.com/blogs/the-staggers/2011/12/issu...
He's also written about this topic here: