Turns out, it is an animated GIF. It seems they autogenerate the GIF with the correct countdown time when you open the email (and thus hit the img src URL in the email HTML).
But, an animated GIF has only so many frames. So really the timer only runs down for about a minute or so. Which means that if you stare at the timer for longer than that, you will see it loop back up and start counting down again.
For the very curious, here is the URL from the email. Clicking on this will generate you a new countdown timer, if you watch it for a minute, you'll see it loop. If you reload, you'll get an updated timer:
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