Amazon's newest streaming stick is missing a Spotify app due to the lack of a native app for Amazon's new Vega OS.
As a result, Amazon has built a workaround for the first Fire TV stick running Vega, which is described as clunky.
Spotify hasn’t launched a native app for Amazon’s new Vega OS yet
This issue is discussed in more detail on Lowpass: Amazon’s new Vega OS-based streaming stick has a Spotify problem.
Author's summary: Amazon's new streaming stick lacks Spotify app due to OS compatibility.