So I just double checked because I find t odd that they would kill support for 8.1 and not 7 when 7 has EOL next month. And you are right. There are no official drivers from AMD for the RX Vegas series of GPUs listed for 8.1.
Hell I even checked the 5700XT, their newest card, and it doesn't have 81 drivers.
My suggestion would be to move on from 8.1 but I know thats not always possible for some people so if you are unable to migrate to 10 then nVidia would be a better option if you go to anything before the RTX 20 series, as those look to only support 7 and 10 as well.
Its odd. Honestly the best solution would be upgrading to 10. If you have a legitimate 8.1 key you can still upgrade to 10 for free.