Technically, no, it's unnecessary, but it makes checking your loops much easier.
Where did you get your version of Goldwave? Never heard of it missing a button before.
I got it from the link you provided within the tutorial. Maybe it's been updated to a newer version since you wrote the section dealing with Goldwave? Mine's 5.57. But, if using the Yellow Play button is unnecessary, then is there some other way to enable a looping playback in Goldwave? Cuz I'm just not finding it.
...Although, I can open the song in Sony Vegas Pro, find the loop points by ear, cut the excess from before the starting loop point and after the finishing, and enable a looping playback to see if the two loop points flow smoothly. Then, I'd be able to save the cut region of the song to be looped as an MP3 that will start from the first loop point and end at the finishing one when opened in Goldwave, eliminating the need to ever use its looping playback function since the song will already start and end with the designated loop points.
If I can do that, I am exempt from performing the "--- Extra Instructions for Custom Looping" step and skipping straight to "---- The 14336 Rule"?