function _arrayBufferToBase64( buffer ) {
    var binary = '';
    var bytes = new Uint8Array( buffer );
    var len = bytes.byteLength;
    for (var i = 0; i < len; i++) {
        binary += String.fromCharCode( bytes[ i ] );
    }
    return window.btoa( binary );
}

but, non-native implementations are faster e.g. https://gist.github.com/958841 see http://jsperf.com/encoding-xhr-image-data/6

jsPerf.com is jsPerf.app now: https://jsperf.app/encoding-xhr-image-data/51

Updated benchmarks: https://jsben.ch/wnaZC

Use this filter to convert byte array to base64

app.filter('bytetobase', function () {
    return function (buffer) {
        var binary = '';
        var bytes = new Uint8Array(buffer);
        var len = bytes.byteLength;
        for (var i = 0; i < len; i++) {
            binary += String.fromCharCode(bytes[i]);
        }
        return window.btoa(binary);
    };
});

to bind it as image use

<img ng-src="data:image/JPEG;base64,{{picture | bytetobase}}" alt="..." width="100" height="100">

Or if you need to assign it a variable use

var image = $filter('bytetobase')($scope.picture );

Your file is a correct ASCII text file with content [\x58595a5052415445454b3123473b4c534e44204e474f49574853474849444748445348474d70253335] literally.
That you get this content when you download it is perfectly fine, since it's what this file's content is.

What you want is to parse that content from the Hex representation they used to an actual ArrayBuffer to finally read that again as UTF-8 text (or any encoding respecting ASCII).

This has to be done after you do download the file and read it as text.
You first extract the actual bytes sequence as Hex from that [\x - ] wrapper, then you split the resulting string at every two chars to get hex values of every bytes, and finally you parse it into an Uint8Array to get back the original data:

// for StackSnippet we need to hardcode the response
// OP would have to make its request return that string
const response = { data: String.raw`[\x58595a5052415445454b3123473b4c534e44204e474f49574853474849444748445348474d70253335]` };
// .then( (response) => {
  const encoded_text = response.data;
  // remove leading "[\x" and final "]"
  const encoded_data = encoded_text.slice( 3, -1 );
  // split at every two chars, so we can get 0xNN, 0xNN
  const hex_bytes = encoded_data.match( /.{2}/g );
  // as numbers (0 - 255)
  const num_bytes = hex_bytes.map( (hex) => parseInt( hex, 16 ) );
  // wrap in an Uint8Array
  const view = new Uint8Array( num_bytes );
  
  // from there you can generate the Blob to save on disk
  download( new Blob( [ view ] ), "file.txt" );

  // but if you want to read it as UTF-8 text, you can:
  const as_text = new TextDecoder().decode( view );
  console.log( as_text );
// } );

function download( blob, filename ) {
  const anchor = document.createElement( "a" );
  anchor.href = URL.createObjectURL( blob );
  anchor.download = filename;
  anchor.textContent = "click to download";
  document.body.append( anchor );
}