I finally found the solution I needed here:

let message = String.fromCharCode.apply(
    null, 
    new Uint8Array(errorResponse.body));

However, because I'm using TypeScript I was getting some kind of annoying message about errorResponse.body not being assignable to type number[], so I'm doing it like this:

let message = String.fromCharCode.apply(
    null, 
    new Uint8Array(errorResponse.body) as any);

Also note that because my response body had an odd number of characters, I had to use Uint8Array instead of Uint16Array. See this helpful answer for details.