It probably lasts the same length of time as the one on their website, as they are both 5000 mAh, so it'll depend on how much energy the gilet uses.
My shawl has three temp settings; it probably lasts 3-4 hours on the higher one, though sometimes it's hard to tell as the blanket turns itself off after a certain amount of time and then I have to remember to turn it back on when I notice it getting colder. I'm not sure what the actual temp or energy rating is, though, as it's just 3 settings.
I think if you want a longer lasting one, you'd have to go for the 10,000 mAh ones or higher. But check the weight on those for sure. The 5000 lightweight one I got was 98g; the one on your site was 210g, so that's a noticeable difference. There are some on amazon I've seen just now in the 10,000 range that are also about 220g, so if that weight works for a gilet (which presumably it does or someone would have mentioned it in the comments), then you could try that. But I was surprised at just how heavy it felt to wear something with a battery pack on one side!
The lighter weight the pack is, the more expensive, and also the more capacity, the more expensive - and I was also concerned about the brands, as I was a bit concerned about fire safety, so wanted a brand I'd heard of at least (though I don't know how much difference that makes).