Here's the way I think it makes most sense.
System is really big: everything we do to make play "go," any procedures at all considered as an integrated total (or sadly not so).
Techniques are specific features of the system, in understandable chunks - this is how my character dies, this is how he gets more powerful, this is how he shoots the goblin in the eye with an arrow, this is how he gets laid ... that kind of thing.
Rules are either what's written down about Techniques, if we're using written material in the first place. Whether you think rules can exist solely in someone's head is up to you.
So, all of that goes to explain that here, mechanics can be either a synonym for Techniques or a specification of Techniques to their distinct physical actions, if you like.
See Reward for an example of distinguishing a System feature from its mechanics-based details. See also The Lumpley Principle for the relationship between any input into play vs. the mechanics associated with it.