That quote is from the judge's decision: he considers that moving violations are quasi-criminal proceedings, and as such, that the protections for criminal prosecution apply, unlike in purely civil cases.

Where is the line drawn for criminal vs civil in nature?

It feels like any civil case brought against an individual by a government is quasi-criminal.

this is why going to court pretty much takes care of these tickets. of course, for a lot of people, going to court costs more money than paying the ticket so people pay.

disclaimer: I write software for court houses and am intimately familiar with the proceedings etc. in some jurisdictions these tickets will be outright dismissed and in others you may have to put up a bit of fight :)

"this is why going to court pretty much takes care of these tickets."

But what about things like red flag laws, child support (like the cited case law), etc?