Why is my Apple Watch Series 3 not updating to watchOS 8.8.1?

If you're on watchOS 6, try and see if you can update from the watch instead

1. Make sure that your watch is connected to Wi-Fi.
2. On your watch, open the Settings app.
3. Tap General > Software Update.
4. Tap Install if a software update is available, then follow the onscreen instructions.

Leave your Apple Watch on its charger while the update completes, and don't restart your Apple Watch. When the update completes, your Apple Watch restarts on its own.

Updating/upgrading Apple Watch - Apple Community

they have a series 2, which goes up to watchOS 6, I'm assuming since it's the device chosen below his question.

Go to watch app --> general --> about and then send me a picture

I can see that Apple Watch series 2 is listed below, You might've mixed with series 2 and 3, Series 2 cannot update above watchOS 6, That is the latest version the series 2 can run, Just looking at the small text below your question: "Apple Watch Series 2, watchOS 6"

You have an apple watch series 2, which supports up to watchOS 6, there is no more above that, your watch does not have the capabilities to run watchOS versions newer than watchOS 6.