I think it hinges on the definition of 'postpartum'. If you're using it in a clinical sense a man cannot ever be pregnant. So he cannot be postpartum. Ergo he cannot have postpartum depression. I haven't a clue as to whether postpartum depression is hormonally linked or not - again if it is then a man can't have postpartum depression. Much like a man can't have PMS.
But men can be moody as shit, there is legitimacy to sympathy pain claims, and men can very much go through depression once the baby is here and if I read that study correctly there's averyhigh correlation rate with women experiencing PPD at the same time their partners do - so you have to look at root cause. Being around someone who is depressed very much can trigger depression with all sorts of other environmental factors going on. So if she has PPD then her root cause is the hormones/actual state of being post partum, whereas the man's root cause can be dealing with a new baby and a wife with PPD - but it isn't PPD.
But I don't know enough about PPD to know whether the root cause is hormonal or not so I can't say one way or the other whether a man can have PPD - it just seems more logical that it would be depression caused by surrounding circumstances since PPD is something that is to my knowledge extremely clinical and is actually just shorthand for a whole lot of PP spectrum issues. I had PPA for example.
All that being said whether its PPD or 'regular' (and I dont mean anything less severe when I say regular) depression, both are serious conditions that can present during those first months (all the way out to 6 months, a year) in both men and women and while they've done a decent job at bringing PPD into focus over the past decade or so with screening and awareness campaigns, and they've done a good job at getting rid of some stigma, I do think there's a deficit of attention paid to fathers in the same time period, and we've got a ways to go on women still too (see further PPA - many aren't even aware that this can happen).