I believe OP shares your sentiments, and that you mistake the usage here.

'Shame' as used here is shorthand for 'that's a shame,' which used colloquially to express disappointment colored with sympathy and understanding, does not imply that any of the nominal subjects is being criticized.

Source: I'm a native English speaker.

Isn't 'pity' fairly similar, or is it more commonly used in British English?

'Pity' would be a Britishism in this context, yes.

I believe this is not the case in the US, at least in my experience. In South Africa people say "shame" to express pity for someone else (or even just when something is adorable) but when I say it hear I get weird looks :)

Native U.S. English speaker here: we do use the word "shame" as GP describes. We use "shame" both to say that someone should be ashamed and also to express general disappointment. (Though we would not use the word to talk about something that's merely adorable.) To my U.S.-English ears, swombat's use of the word "shame" seemed clearly of the "general disappointment" variety.

In the U.S. don't we generally use "for shame" when berating?

Yes. But here the writer simply began a statement with the word "shame" and proceeded to give a sober explanation consistent more with disappointment than outrage. In this context, I think the better interpretation of the writer's sentiment is to read "shame" as, essentially, short for "it's a shame" rather than "for shame!"

No, it is definitely a case in the US. In his sentence, you could expand it to "That's a shame" or "That's a crying shame", both idioms that can express that something is "unfortunate" or "disappointing", and does not always require a blame.

I'm a native English speaker and I was born and raised in the US (specifically the Pacific Northwest), and "shame" isn't weird at all.

It's used to express disappointment – with or without blame.

Thanks for the responses everyone. I've been in the US 15 years now and I'm still never 100% sure about dialect differences :)