Identify this peg game?
I'd guess it to be a tic-tac-toe variant in which you can (re)move pieces. Players play normally with seven pegs, but three in a row or some other pattern allow you to capture an opponent's piece which goes into the hole.  Player with most pegs on board wins. 

Couldn't find anything exactly like this at BGG.
https://www.boardgamegeek.com/geeklist/16886/games-played-3x3-grid