Record your PowerPoint slide show using built-in PowerPoint functions:
Record using PowerPoint -->Slide Show -->Record Slide Show features: Office Support Tutorial 1, Tutorial 2
Record using PowerPoint -->Insert --> Screen Recording features: Tutorial
Record using above method (save as PPTX) and export to video: Tutorial
You must save as PPSX in order to let other computer to be able to play the sound.
NOT PPTX.
After you have successful finish your recording, please click save it again, and then save as PPSX file.
It is not necessary to convert this PPSX file into video file. Now, with this new PPSX file, other people can directly plays like video.
If you are using the first method, and there are no audio comes out, please change this PPSX file back to PPTX file again, then it will become a normal slide show with speaker icon on every slide. In that case, it will have sound.
If that haven't solve your issue, please try to create a new PowerPoint file and then record your original PowerPoint file using Method 2. (Record Screen)