These are two distinct questions. Are Obelisks part of the self? If you think of the "host" as being made up by it's DNA, then these are not part of that set, since they are not found in DNA copies. Or is an organism it's RNA? If it's the RNA that's the organism, then sure you could say this is part of that organism in that it exist as organelles of sorts, like mitochondria or chloroplasts (but in RNA form).

The second question is if it's parasitic, mutualistic, or neutral. If it's a parasite it should cause a fitness defect to the DNA organism's replication. As of yet I haven't seen evidence of this at the cellular level. But there is a strong argument that by depleting cells of nucleic acids (RNA) would have to be at least minimally parasitic. That is of course unless they confer some advantage to the cells with Obelisks. In which case, why don't all microbial cells have Obelisks. Importantly, the relationships between all the various Obelisks at least for now, is not lining up with microbial genome evolution. This would mean they are jumping from genome to genome.

Now you're in a late night pub discussion about where we should be drawing the boundaries of life.