Someone who gleefully shoulders a mountain load of tech debt at 2AM on a Saturday morning?

It's VC-talk for someone who does stuff at a company.

I'm assuming it relates to operations management but I imagine this type of person not accidentally taking a little shine from the name collision with spec ops soldiers and Matrix movie characters

It is leadership speak for one of the four archetypes. Visionary, operator, processor, synergist.

In other words, four words to make people feel good about their role at a company. Middle management is littered with these obscure definitions.