There's no need to justify how you do business with the NYT, whether it's playing a crossword game or accepting a job. But either one is referred to as crossing the picket line.
Surely playing a crossword game is only "crossing the picket line" if the workers on strike have asked you not to play that crossword / called for a more general boycott?
I think there's a deeper and more important subtlety here: there's a sort of moral obligation not to break a strike, but except in some specific circumstances, there really isn't an obligation to support a boycott, any more than there's an obligation to put a pro-labor bumper sticker on your car. Breaking a streak and ignoring a boycott are not equally weighted.
(My kid brother is a labor person, so really I'm just venting some stuff here to keep it from coming up at Thanksgiving).
The way you're using it, it sounds like a pejorative... Which puts something of a spin on your particular pedantry here.
> there really isn't an obligation to support a boycott
I think the Irish - who invented the term - would disagree with you on that point.
Not every boycott is worth supporting, sure. But if a boycott is worth supporting (say, divesting from genocide supporters) then yes there's a bit of an obligation there.