Google Quality Score Algorithm?

I just read on the SEROUNDTABLE here, about the Google Quality Score Algorithm. When google talks about quality score, are they talking about The MOZ rankings DA & PA? Are they related somehow?

Google measurements will have nothing to do with MOZ rankings which are unrelated numbers that somehow have captured webmasters attention as being viable metrics despite having nothing to do with any search engine.

The Google Quality Score has go do with the adverts, landing pages and target sites for ads in the Google Adwords scheme.

Here is Google's own definition of it.
https://support.google.com/adwords/answer/140351?hl=en

With so many blackhat and rubbish pages dominating the serps, I've stopped listening to what google is saying.

As Gooner says, it's related to adwords.

The theory (and I believe it works this way in practice) is that the better your ads perform (clicks against impressions), the higher your quality score goes. The higher your quality score, the less you have to pay per click to maintain the same position or better in the ad listings.

One of the reasons you should pay close attention to how you craft the wording of ads. A consistently high performing ad gives Google a better overall return, and they reward it by making it (slightly) cheaper for you.

I thought Google had some pretty tough restrictions when it came to adwords and gambling advertisement?

I think the OP is probably referring to the metrics that Google uses in Analytics like Bounce rate, time on site etc. I notice that they've started sending out monthly emails highlighting these figures to site owners, so I guess ranking factors are fairly heavily weighted to these stats now.