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"Network monitoring system" makes me think of routers, switches, Mbps / Gbps, etc. This seems more like a "server monitoring system."

Nope as well. It's more a stream processing engine. Icinga/Nagios or Zabbix are (inflexible) specializations of such engine.

Servers are on the network as well... and the phrasing is more towards the "network" as an environment.