No, you do not need an external DAC.
You will, however, need an external amp. If you search this on Amazon, you'll find the one I got: 2 Channel Stereo Audio Amplifier Receiver Mini Hi-Fi Class D Integrated Amp 2.0CH for Home Speakers 100W x 2 with Bass and Treble Control TPA3116(with Power Supply) - Fosi Audio TB10A
This is more power than these speakers require, but it works fine. If I connect the amp to my laptop and connect the speakers to the amp, when I have my laptop's volume and Spotify's volume all the way up, I have a comfortable listening experience, maybe 60 db, from about two feet away, and the amp's knob is almost off (at most 1/10th of full volume). I live in a small apartment. If I turn the knob past about 25%, I'm sure my neighbors can hear it. So my solution is to turn my laptop's system volume as well as Spotify's volume down to 50%. When I do that, I'm able to have more control over the volume using the amp's knob and I'm comfortable with the knob turned to about 33%
You could probably go for an amp that provides 50 watts per channel and be fine.