It refers to animal-years, yeah. (IMO the choice of words is okay, even though it could have been clearer; 10 years = 10 animal-years is is the only reasonable interpretation, so I don’t think there was any intent to mislead.) I’m not sure it’s quite right, though; it’s actually an underestimate, according to the Lewis Bollard quote that it seems to be based on, but on the other hand Bollard seems to be referring to the costs and benefits of one specific campaign, rather than to anything that could reasonably be taken to apply to ‘every dollar donated’. So I’m not sure if it’s just a rough ‘averaging out’ of those two factors, or if it’s based on more details that I missed when I looked at the transcript.
In the transcript of the podcast, the relevant section is at around 32 minutes. The specific claim seems to be that they spent <$200 million on a lobbying effort that directly caused reforms that so far have spared 500 million hens (and are continuing to spare 200 million per year) from battery cages and have improved the lives of billions of broiler chickens (>1 billion per year), over lifetimes that aren’t exactly specified but that result in “a ratio that is far less than one to 10 of a dollar per year of animal well-being improved”.
edit: a quick search suggests that the lifespan of a battery hen is a little under a year and a half, and the lifespan of a broiler chicken is a month to a month and a half. So I’m not sure exactly how those numbers work out; maybe the <1:10 ratio depends on the assumption that the benefits will continue into the near future.
That’s why it’s presented as a prayer, I think. It’s not a One Weird Trick or even a piece of advice; it’s more like an acknowledgement that this thing is both important and difficult.