Hi there jujubad,
Per Transfer your AppleCare plan (that you've already looked over):
If you receive a replacement device
If we replace your device instead of repairing it, we’ll automatically transfer your plan to your new device. If transfer of coverage isn’t possible, we’ll offer other options.
If the AppleCare plan is still not transferred to the replacement AirPods after you return the defective ones to our service center, then contact Apple Support next. They would be the best equipped to look into this further with you. Reach out using this: Get Support
Cheers!