In NFPA 70E table 130.7 it is stated that normal operation of a well-functioning circuit breaker/contactor does not require any PPE (unless there open doors/covers). And the conclusion is that there is no need for Arc protection as longs as everything is working correct. Does anyone if the NO is related only to circuit breakers that are arc resistant?

On the next page they calculated the PPE value for Nema E2 fused contactor so I think it is a bit strange…..

It sounds like you may be working from the 2015 edition which is inappropriate after issuance of the 2018 edition on August 21, 2017.
To answer your question, the PPE Required Yes/No table 130.7(C)(15)(A)(a) and (b) are replaced in the 2018 edition with the 130.5(C) likelihood of occurrence table. Normal operation is defined in that table and as long as those requirements are met, you can operate a standard cb without PPE, or at least the table says there is no likelihood of occurrence. Your Electrical Safety Program would have to endorse that.
2018 edition Table 130.7(C)(15)(a) designates that arc-resistant switchgear at 1000-15,000 Volts with doors closed that meets the listed criteria does not need PPE to interact with (N/A) because the incident energy level is less than 1.2 calories, formerly PPE 0.

There is no "expiration" on different editions. There is simply a new edition out there. OSHA's Subchapter S is largely based on a version from 1986 if I recall correctly. NEC adoption is even worse. MSHA only recognizes one section of the NEC from the 1970's and has never advanced since then while state adoption spans the gamut going back over a decade in terms of editions. As a voluntary standard, NFPA 70E has even less standing as far as mandating one version over another. Nothing in any of the editions "expires" older ones. It is up to the end user to decide which editions to adopt.

Second, arc resistant gear can have an arc flash with the doors closed and bolted shut with no severe injury even to someone standing right next to it. So it gets a "no" rating.

Operating breakers whether arc resistant or not stems from the very low failure rates if they are maintained properly. So as an example even though being struck by a meteor is fatal, we do not erect meteor barriers over our places of work simply because the likelihood of occurrence is so low that it is a waste of resources. Similarly properly maintained circuit breakers rarely fail in a way which would cause injury (arcing fault). With very low failure rates, no PPE is required.

As a real world example a chemical plant in North Carolina refuses to maintain their switchgear. As a result around 10-15 years ago an electrician was severely injured by an arc flash and spent several months in a burn unit when he closed in the breaker and it arced and failed. The solution that this plant has adopted last I knew rather than properly maintain their equipment is simply to wear 40 cal/cm2 suits while performing maintenance or even operating the breakers rather than take the downtime to maintain them properly.