I think this broadly depends on what role you view art critique as having. In the opening paragraph, the author does a great job (IMO) of outlining his perspective:
"As a critic, I’ll suggest that I can sensitize my readers and listeners to what they didn’t see or grasp or apprehend when they witnessed the same art or performance."
If you view critique as a way of exploring new perspectives, subtle context can be one of the ways in which a critic can help add to the conversation surrounding a work. While it's not necessarily a critic's responsibility to understand every piece of background info at every moment, it's also understandable that a critic might view their own omission of a particular piece of context as a failure to provide additional insight that they believe they might have been able to contribute in a review, especially they view the goal of their critique to be that act of "sensitizing."
> More broadly, does great art have to be immediately striking and accessible?
Part of what Rodney might argue here is that it's not necessary for art itself to be striking/accessible, but a good critic can make such art accessible by virtue of dedicating themselves to the understanding of "subtle contexts."
> If a piece of art resonates only with people who share the artist's context (like the mentioned punning pronunciation of "boy" in a given dialect), can a critic lacking that context review it, or a viewer appreciate it?
I'd argue that context isn't a strict requirement for appreciation, but that it can often be a useful way to construct additional meaning, to find additional appreciation for a work beyond the initial appraisal. It's different for everyone, but I love art and art critique, and these are the ways of thinking that I've personally found bring me the most joy/fulfillment when thinking about art.