Uh-Huh is correct when he advises that you don't begin work unless you have a Z-visa.
That said, this is China and there are many things that are possible. You can't get a Z-visa unless you have an authorised degree is akin to saying that you can't walk across the road when the 'little red man' is on red.

You have an associates degree and that is highly likely to be regarded by many prospective employers as being 'good enough', especially in the current climate where ESL teachers are in short supply. Many schools will 'cross the road while the little-red-man is lit', just to get teachers.

As long as you have a decent TESOL qualification and are a NES, then you shouldn't have too much trouble in finding work. However, I must re-iterate what 'Uh-Huh' said below, don't even THINK about starting work on anything other than a Z-visa.

The YouTube video that you highlighted in your OP was submitted back in March when no-one knew for sure what the ramifications of this new law would be. She also says that she has already been teaching in China for 4 years. This would take us back to around 2012 when this rule was easily ignored or just simply wasn't in force.

Now that it IS being enforced by the PSB in many provinces, FT's are leaving China in droves. Someone will hire you, a training centre most likely, but don't sign a contract with any of them without first posting your intentions on such a forum as this. At least that way you have a good chance of getting at least SOME advice as to whether your prospective employer is well below the level of a snake's belly, or on par with one. Good Luck !