The WIIM streamers, or any other streamer, resides on your home network, either wireless/wifi or wired. You can control the streaming app from your phone or a computer. In the streaming app, such as Spotify, you select where the music is going to play. You would choose the WIIM streamer, select the song/track/album and hit play. The music files are played by the streamer and it is output to whatever you have the streamer connected to. In this case, you would have the WIIM connected to your DAC, and the music will play on the speakers connected to your integrated amp.
If you get a streamer and want to use your DAC, you'll just need to insure you have an available input on your DAC and you have a corresponding output type on your streamer. You are using an optical connection from your cable box to your DAC now, correct? You'll need another optical input on your DAC if you need to use an optical output from the WIIM Mini. The WIIM Pro has a coax output as well as optical, so you could use a digital coax cable instead of optical. Will work exactly like to optical connection.