Let's talk about some basics. First this happened in the tunnel where the LHC is now, but it was a completely different machine called LEP. This happened in the 1980s which means that computers were slow and expensive compared to today as was 'fast' digital storage (tape was not to expensive to use in bulk but it was very slow). Digital readout of detector response was managed with simple ADCs protected by hardware vetos during relatively wide readout windows (and with hardware delay lines and other compromises that look incredible from our privileged vantage point).
As a result large scale experiments had to be highly selective of the data they captured and stored permanently. And the triggers that made these decisions were built in hardware: wires and simple digital logic circuits (ORs, ANDs, etc).
They asked simple questions like "Did the projection chamber show a large response in at least 3 sectors?" (3) and "Did we get a significant response from time-of-flight subsystem in opposite quadrants?" (1).
The triggers that you have described above rely on fast elements in the detector (the hodoscope-based time-of-flight system and the high-density projection chamber) and just ask if they've seen activity in widely dispersed angular directions (which is what you expect from the decay of $Z$ generating annihilation).
"Efficiency" can mean a lot of different things, but without seeing a detailed description I would guess that they take a low bias sample (accept a small fraction of events that don't generate a physics trigger so that they can convince themselves that the triggers aren't losing important events), and that these value represent a best guess at what fraction of event the trigger should have responded to it did respond to (the rest are lost to cracks in the detectors and to not quite meeting thresholds).