The bit about uniqueness seems like a good way to get happily boring, yet otherwise professional people to spiral into an identity crisis.

The dichotomy as presented is IMO a good one to question; for example we could guess that "experienced engineering team player" would play better than "team player" for an engineering team position. So what else is out there that's not going to require uniqueness in past position, yet offers promise in writing?

(Also did Acme Games have only one employee, or...? Otherwise this unique-to-you perception seems a bit inequitable)

Not so much about being unique as about being credible. Specific claims are more credible than general claims.

I feel “experienced engineering team player” does not sound credible. We know this about ourselves so we don’t question it. But from the outside in, there is no value in this.

On the second point, Acme Games was an example. If you say, Software developer at Uber, that has immediate credibility. People assume things about you.

I am surprised when I see resumes where people go on and on about how experienced they are and list programming languages and modules in their resume summary but don’t mentioned where they went to school or where they worked until much later in the resume.