I think it's fair to count the number of missions (it's at least consistent across engine types), though I'd probably prefer to also see the number of engine-missions as well.

But in defense of counting the number of missions, each mission has similar "external" characteristics: ambient temperature, sunlight level, burn duration, wind shear, humidity, etc. A combination of these environmental characteristics could cause a failure (Challenger failure was caused by excess cold). Since the environmental characteristics are the same for the mission, the number of distinct missions an engine has performed is a decent proxy for robust performance throughout the space of environmental conditions.