Author makes some decent points, but I'll respectfully disagree.
For the "increment a thing" case, you could CRUD and create an "interaction request", which is digested later to later do exactly what was requested. This avoids breaking the REST principle at all--you simply treat the high-level semantic operations as their own objects. Now, whether or not this makes your API and design bloated is a different question; that said, it does fit nicely with REST.
Most of their other points have a similar rebuttal: problem is not using REST, but instead using it at the wrong level.
For the "increment a thing" case, you could CRUD and create an "interaction request", which is digested later to later do exactly what was requested. This avoids breaking the REST principle at all--you simply treat the high-level semantic operations as their own objects. Now, whether or not this makes your API and design bloated is a different question; that said, it does fit nicely with REST.
Most of their other points have a similar rebuttal: problem is not using REST, but instead using it at the wrong level.