The term "old-school" has two decidedly different meanings. On the one hand, it can mean classically trendy, something that never went (or will go) out of style. On the other, it connotes something that's outdated, outmoded, and fairly irrelevant.
I cut my teeth on ping and SNMP, so — while it pains me to say this — old-school monitoring is decidedly in the latter category. Back in the day, if the experience your company was providing, I’ll call this a service, could be measured, it was not easy to do. You were left trying to infer user experience based on data from parts of the service as a whole. It included measuring CPU, RAM, and database metrics and hoping that those metrics reflected enough to tell whether your service was truly working for your customers. With this “old school” way of thinking, enough tangential insight could add up to a full picture of a user's actual experience.