Spotify's music files are protected by DRM, which can be troublesome for those who want to enjoy Spotify music on any device as they wish. Therefore, if you want to play Spotify music on your TV, the most important thing you need to do is to record Spotify music to get DRM-free vesion.
You can try AudFree Spotify Music Converter, which can help you record Spotify music, download music from Spotify for free and convert them to MP3, AAC, FLAC, WAV with 100% original quality. Afterwards, insert the USB stick into the USB port of your computer and copy the converted Spotify music into it, then insert the USB stick into your TV and you can play the wonderful Spotify music.