It literally makes playing the game impossible once it is triggered. There are several threads— both on this subreddit and on the Warframe bugs subforum— that have been trying to get this issue addressed. One Tenno even figured out a way to trigger the auto melee bug on command to prove it existed. And it shows just how easy the bug can be triggered. If you melee too quickly after casting an ability associated with the melee button, you're now stuck in permanent auto-melee for the rest of the mission. Auto melee has been bugged since it launched and it hasn't been addressed yet :/
Hiho!
Could you explain what you mean by being stuck in Auto-Melee for the whole mission?
The video that you linked shows being able to stop the bug by pressing Melee again. To my knowledge that's how almost all open Auto-Melee issues work.
Are you perhaps thinking of Operator stuck in Void Blast? That one got fixed with Update 35.1 on the 20th.