Raising prices then checking if so-called "competitors" follow is the illegal part - that's automated collusion, definitively illegal.
There is grey area around intent/motive, but the OP article is clearly on the bad side.
(Also, "standard practice" doesn't mean legal or moral)
This is completely false. Collusion, legally, requires an agreement between competitors. Tacit collusion is *not* illegal, see Brooke Grp. Ltd. v. Brown & Williamson Tobacco Corp. (1993).
Amazon can raise and lower their prices all day, algorithmically or not, as long as they aren't calling up their competitors and telling them to raise their prices too.
It is not unkown for 'competitors' to stage cost cutting dramas and pantomine competitive pricing in order to create artifical demand and customer loyalty to either or both scrappy underdogs.
This is a form of automated collusion. I'll raise my price and if my competitors don't follow suit I will lower it again. It only works well for them if the competitors are watching prices too and looking for an opportunity to raise theirs. You know it's anti-consumer because of the conditional reversion after watching competitors prices not following.
I have a feeling there is currently a LOT of this going on across all industries in the US. We've seen it rent pricing software, now Amazon, and I think fast food and restaurants are dojng something similar. Food has gotten obscenely expensive expensive outside a grocery store.