Interesting article. Machs principle has been debated since before Einstein. Even einstein pondered it deeply.

I think theres merit in machs principle and perhaps a thruster uding it is possible. But you're still looking at six year or so just to get to proxima. Assuming you're not traveling at light speed or close to it a significant amount of time your enroute. Then what a few months on station and then another six years round trip. Its still pretty impractical.

I think looking at machs principle in a different way would be more useful. Like what if you thwart it entirely. Obsfucate your reference frame so in a way the surrounding universe doesnt really catch on that you're moving. A decoupling in a way. If the universe doesnt realize youre moving does it then matter how fast you actually move or accelerate?