Does the peer review reciprocity principle apply globally or per venue? It is commonly accepted within academia that if you submit and publish peer-reviewed papers, you should also do your share, and review your peers' papers.

Does the underlying principle apply globally or per-venue? Should you aim to do approximately as much review work as your own papers received, considering the total sum of all your contributions in your field? Or is there a social convention or moral obligation to do peer review work in the same venues that you submit or publish papers in?
First, I'd say that your obligation* of peer review is to help your community of peers, not specific venues or publishers. It's the peers that do the reviewing mostly for free, and their work you're supposed to reciprocate. Hence the principle should apply globally. 

However, spreading your efforts out a bit can be beneficial, leading to more diverse reviewer pools for a given journal. (And hence a higher chance they can find the ideal person to ask.) And of course, you're free to focus your efforts on reviewing for journals you particularly like, whether for their quality, (possibly also unpaid) editors you have a good relationship with, or other reasons.

Second, aiming for a close balance in reviewing efforts given and received seems misguided. Focus on writing useful reports, not on the amount of work (that of others is hard to estimate anyhow). You can't really review more than you're invited to review, and even then it's certainly better to decline if you can't produce a quality review in the expected standard time frame than accepting each invitation in a vain attempt to cancel out review work you've received already.

*If obligation is the right word. I tend to think of 'obligation' as a requirement, whereas this reciprocity is more of an 'ought' in my opinion. But hey, different definitions exist.