Recently published paper deliberately not citing our very relevant work -- anything to do? Note that the difference between this question and a related question (Recently published paper does not cite my very relevant work) is that the authors in my question are fully aware of our work, whereas, in the related question, the authors were not aware of OP's work.

A recent paper did not cite our very relevant work. 

There are significant overlaps among the scopes of the papers, and one of the important figures and the related conclusion are almost identical.

The leading author of the paper in question has been informed about our work even before we submitted the paper. I've asked for a reason for not mentioning it, and the answer was that our paper was noticed during the revision of the paper, and the authors do not feel obliged to mention it. 

Is it OK to not mention a paper because of ``seeing it too late?''
Regarding this: does the date of submission/acceptance play a role?

Our publication date is before their submission date.
You have no real recourse. Authors can cite what they like and snub others for no reason. Plus, you can't cite everything so someone's going to get left out. But if it seems purposeful it very well may be. I would send your paper(s) to the snubbing PI and say something like 'looks like these slipped past you'. 

It's in their best interest because of your work truly is that related, you'll probably review their papers eventually.