The term has potentially as many specific legal meanings as there are statutes that use the word. One example is title 29 of the United States Code, chapter 7 (Labor-Management Relations), which defines "strike" thus:
The term “strike” includes any strike or other concerted stoppage of work by employees (including a stoppage by reason of the expiration of a collective-bargaining agreement) and any concerted slowdown or other concerted interruption of operations by employees.
Which is not terribly helpful. Also unhelpful is the definition of "employee":
The term “employee” shall include any employee, and shall not be limited to the employees of a particular employer, unless this subchapter explicitly states otherwise, and shall include any individual whose work has ceased as a consequence of, or in connection with, any current labor dispute or because of any unfair labor practice, and who has not obtained any other regular and substantially equivalent employment, but shall not include any individual employed as an agricultural laborer, or in the domestic service of any family or person at his home, or any individual employed by his parent or spouse, or any individual having the status of an independent contractor, or any individual employed as a supervisor, or any individual employed by an employer subject to the Railway Labor Act [45 U.S.C. 151 et seq.], as amended from time to time, or by any other person who is not an employer as herein defined.
In fact, it is not usually necessary to observe statutory definitions of terms when discussing something that is outside the scope of the statute in question. Lawyers will nonetheless counsel their clients to avoid doing so because they do not want the use of the word to be taken as an implied admission of some circumstance that might weaken the client's case.
I don't suppose the striking moderators are actually employees of Stack Exchange, Inc., so I cannot imagine how using the word "strike" could cause trouble. But that doesn't matter a whole lot. If they don't want to use the word strike, they can refrain from using it. If they're trying to spin the situation by hiding behind purported legal advice, the only way you're going to prove that is with direct evidence. Even if the legal reasoning is bogus, it could just be that they have a bad lawyer, or just an overcautious one. Maybe they are worried that SE using "strike" would trigger a requirement to pay moderators minimum wage. Or about something else. Or maybe it's just spin.