It might be spamming domains because it can't reach anything because it's blocked. Unfortunately this means it ends up dominating the Query Log. Here are a couple of ideas to try.
Go to Domains and create a wildcard whitelist entry for uaid.nmrodam.com by copying and pasting it into the Domain line and ticking the wildcard box and clicking Add to Whitelist. This will allow all these weird domains to be queried. This may satisfy the Fire TV stick and so it stops asking once it's had a proper DNS reply.
If the Fire TV Stick is still making too much noise in the Query Log, another option might be to simply not use Pi-hole for that device. You can edit the Fire TV stick's DNS to use either your router's DNS or a public DNS such as Cloudflare's 22.214.171.124. Now it will send its queries there instead, keeping Pi-hole clear. But note that you won't have any blocking on that device now.