In a nutshell, is this basically "stress the part and it wears out faster"?
It’s more like “stress the part and that part will change its internal maintenance processes, with some ripple effects across multiple parts”. They didn’t even find a consistent stress=aging pattern across multiple tissues.
No, the article specifically mentions that some parts appeared to experience the opposite of accelerated aging. Presumably that means the “parts wore out more slowly”.
You might be interested in “hormesis”, a vital aspect of Life’s resilience, in which (some) stress improves a system.