This isn't a literal labor-law situation, and I don't think anyone is confused about that.
However, language and communication sometimes requires people to adapt words to best-match a concept which may not have a precise word for it yet, or in order to provide a less-convoluted way of quickly referring to something.
In this case, "strike" is a commonly-used and well-accepted colloquialism for "people mutually-refusing to do something".
Furthermore, if you abstract-out your thinking even slightly, queuing for a Duty as Healer absolutely is a form of "contract" with "the designers", wherein you agree to:
- Enter the instance in a timely manner when your queue notification arrives
- Participate in the content to the (hypothetically) best of your ability
- Coordinate with your Party as-necessary to complete mechanics
- Provide all necessary services of the Healer Role
In exchange for complying with these expectations, you are rewarded with compensation such as:
- Approval to continue your Quest Storyline
- EXP
- Currencies
- Equipment
- Cosmetics
- (etc)
Potentially, some people do this "solely for fun". However, I suspect that if Duties were not required for Storylines, and both baseline Duties and Roulettes offered absolutely zero rewards besides "gameplay experience", then queue times would probably reach the order of days or months.
ie — Duty Finder is obviously perceived, and used, as a compensated service, in which Players agree to do something in exchange for a promised reward. Furthermore, this is implicitly expected to be done on a regular schedule, in order to ensure the overall functioning of a wider system.
This is close enough to a system of "work" — if not formal employment, then at the very least, "gig work" — that it is not unreasonable to apply labour-related terms to contextualise it.
In fact, it's something of a commentary on how dreary the experience has become for many Healers in FFXIV that they intuitively jumped to "labour" terminology when deciding how to refer to the situation.
Fantastic, it has even more in-common with a lot of real-world jobs, then.