[nbm]

Perhaps the right word is “system” - the combination of software (DNS protocol server software, health checker, BGP agent, and so forth) involved in making the DNS service available (or not, in this case). These could be running on the same computer, or separate ones if you are particularly imaginative.

Unfortunately, “DNS system” means something very different than if you said “load balancing system”, so “server” is simpler.

(Usual disclaimer: work at FB, even on this exact stuff, but not representing it.)