As contextually hinted here in the sentence "1838 – "Instead of having treed their game....", the meaning of possibly rarely-known phrase "tree his/her/someone's/their game" has some positive meaning like "mastering the game", which if not realized, it suggests futile and ignorant efforts or course of action(barking up wrong tree).
Now this usage of the word "tree", I haven't come across even after much efforted searching of it's phrases' list or origins.
Can someone confirm whether the contextually hinted meaning is correct and accurate and also explain when and by what origin, the word "tree" was used to suggest positive meaning hinting "mastered/well-understood their game" ?