I was having this conversation yesterday. The criteria you've given is required for an organism, a subset of life. The article I was discussing made a case for a self replicating, unbounded molecule as the first "life entity", making it a second subset of life, distinct from an organism. Following this logic, aa RNA virus is life like, as well as a computer virus, provided the ability for random mutation is present. I don't know if any software can truly make random sequencing errors like a nucleotide polymer.

That was my argument away.

About purely electromagnetic life, I would have to think hard about that, matter is just a collection of interactions with fields.