Reaching that conclusion is pretty simple. At least simple and straight forward enough to charge someone. Probably not as simple to get an actual conviction.

I think this is what happened. They probably found several cigarette butts inside the perimeter of the vandalized private property, they ran DNA tests for all of them and one matched this guy's DNA. There are only a few possible reasons for his DNA to be inside that perimeter:

1) He was a contractor doing work for the Dakota Access Pipeline operator (probably already ruled out, otherwise he wouldn't have been charged).

2) Somebody took his butt from outside and put it inside the perimeter (very unlikely).

3) He actually smoked that cigarette and dropped the butt in that location while he was vandalizing it (most likely scenario from the prosecution point of view).

4) He trespassed the property at a different time and smoked and dropped the cigarette butt at that time. This is still an unlawful behavior but is probably better than all the other charges. (This is a possible scenario but it would be pretty hard for his defense to demonstrate this is what actually happened).

Again. This is enough for prosecutors to charge this guy but it doesn't mean at all that this is good evidence to get a conviction. In my humble opinion, a cigarette butt with your DNA is pretty weak evidence in this particular case.