Great photo. There is some past discussion of this image on the web.
https://www.baseballhistorycomesaliv...ox-ball-field/
The field is the current “Green" at Dartmouth. Right in the middle of town. That line running from the left of the batter to the right of the shortstop is a footpath across the Green.
Dartmouth played Harvard on May 23, 1882, in Hanover.
Below is a boxscore from an earlier 1882 game, May 17th, between Harvard and Dartmouth, in Cambridge.