Dexter Industries Raspberry Pi Speaker

I purchased a Dexter Industries Raspberry PI Speaker and it does not have a compatible plug for the Raspberry PI. PI = 4 conductor 3.5 mm, Speaker = 3 conductor 3.5 mm. This does not seem to be compatible.

It is compatible. The A+, B+, Pi 2, Pi 3 and Pi 4 all use the same 4 pole socket. (The fourth contact is for video.)

I understand that all Raspberry Pis use a 4 pole connector. Why does the speaker the speaker use a 3 pole connector?

Until a DI engineer responds to you: My guess is to mix the left and right audio channels for a mono speaker? (Ground, Left, Right)

Perhaps you could test by:

aplay /usr/share/sounds/alsa/Front_Center.wav
aplay /usr/share/sounds/alsa/Front_Left.wav
aplay /usr/share/sounds/alsa/Front_Right.wav

btw: getting your audio setup can be interesting also. This is how I test mine:
=== first see if audio output works the way you want (auto) ===
Test audio out:
aplay /usr/share/sounds/alsa/Front_Center.wav

===== If no sound: Set output device for desired audio output device (0=auto, 1=analog, 2=HDMI):
amixer (to see current setting)
sudo amixer cset numid=3 1 (set to output sound to 3.5mm jack)
(up arrow till) aplay /usr/share/sounds/alsa/Front_Center.wav

========== If audio output is too soft =======
if soft: alsamixer
s (select card)
downarrow to “0 bcm2835 ALSA”
8 (4=default loudness, 8=100%, 9=125%)
fn-F6 dn to USB Audio Dev
8 for 90% then up-arrow for 100%

      Escape (press Esc)

then make setting default:
sudo alsactl store 0