Is a person with an EU work permit considered a citizen of European Union Member States?

The page you are linking to is at least ambigious and if you check the neighbouring page on temporary restrictions (section 10 - Polish Borders), they kind of contradict themselves. Internal EU borders were opened completely on June 13th. Since then, all travel, also for tourism or fun, from all other EU/EEA countries has been allowed without restrictions.

On that page, it is also more clearly written, that the list of exceptions you are quoting from applies to people entering Poland from outside the EU. If you are in the Netherlands now and travel to Poland, these exceptions are not relevant for your case.

I was a foreigner who lived in a EU member state. You are living and working in Netherlands. So, to travel to another EU member state/Schengen country/Switzerland, you need a valid long-term Visa or a residence permit of Netherlands (or any other EU/Schengen country). As far as I know, a work permit is not accepted as a valid entry document for non-EU citizens in many countries.

Note. The question is tagged covid-19, but the title and body suggests that the question is general. Note 2. The question title "is ... considered citizen?" is different from the body which deals about the ability to travel. I will not take the COVID-19 pandemics into account for the answer.

The answer is very simple. First, you are no EU citizen with a work permit. Second, you can travel freely within Schengen Zone, of which both Nederlands and Poland are members.

By being legally in the Nederlands (thanks to the work permit) you already cleared all sorts of immigration. You can move freely.

No border control is done between states (except for pandemics), so air carriers may just verify your identity but cannot decide on your eligibility to stay in the Schengen Zone.

You can't work or settle in Poland (unlike me for example). Only EU citizens are allowed to move to other states for reasons of work. You would need the EU citizenship. And you wouldn't even need a passport in that case, because a National ID is fine.

The 90/180 days rule applies when traveling to different member states.

Sources

I have queries Traveldoc.aero. To make things more difficult, I selected Zimbabwe as passport nationality. Result is Passenger is travelling within the Schengen Area: no applicable immigration requirements.

Wikipedia about the Schengen Area

For flights within the Schengen Area (omissis), law enforcement agencies, airport authorities and air carriers are only permitted to carry out security checks on passengers and may not carry out border checks. Such security checks can be conducted through the verification of the passenger's passport or national identity card: such a practice must only be used to verify the passenger's identity (for commercial or transport security reasons) and not his or her immigration status. For this reason, law enforcement agencies, airport authorities and air carriers cannot require air passengers flying within the Schengen Area who are third-country nationals to prove the legality of their stay by showing a valid visa or residence permit.

Note about COVID travel

To my record, while there are known limitations to travel because of the pandemics, all restrictions are based on the purpose of the travel and not by immigration status of the traveler. For this, the answer shall not change between pandemic and post-pandemic era.