Yes, your Mac is a ’streamer’. That’s all streamers are - computers. As long as the bits are getting to your DAC without error, then you have a fully functioning setup. There’s no need to buy another box.
I currently use a Mac mini as a streamer for a living room system and a Raspberry Pi 4 for the downstairs stereo. The Mac holds all my music in a shared folder. The RPi can access the shared folder and streams my music library over wi-fi - everything from ripped CD’s to hi-res 24/192 downloads to archived SACDs without a hitch.