Here is a photo of some pieces excavated from the Lothal site in northwest India during the 1950's-'60's. These pieces are often referred to online as from a "chesslike game", discovered at Lothal. It’s probably fair to say that some kind of board game(s) was played at Lothal, part of the Harrapan or Indus Valley civilization that thrived from about 2600 BCE to 1700 BCE. We know that the Indus Valley people had trade contacts with Mesopotamia, Egypt and the peoples of the Persian plateau and all of those people played board games. In Mesopotamia, there was the game of 20-squares, imported by Egypt, where the 20-squares boards (in somewhat modified form) were often on the other side of a 30-squares game called senet. In the Persian plateau stone game boards have been discovered at Jiroft – not all of which are frauds. And there was the magnificently carved wooden "serpent game board" discovered in excavations at Shar-i Sohktah – a variation of the 20-squares boards excavated by Woolley at Ur.
Trade contacts over a 900 year period would no doubt have led to the introduction of board games into the Indus region from any or all of these regions, even assuming their civilization had before then been unfamiliar with the concept and did not produce their own board games. As far as I am aware, however, no game boards were excavated in Lothal, or at any of the other Indus Valley sites. This does not mean that the people there did not play board games; it may simply mean that they made their boards out of materials that did not survive the ravages of time.
And so we are left with these pieces, many which resemble game pieces discovered in Egypt, Mesopotamia and Shar-I Sohktah. Did the Lothal residents play their own unique board game with them? We don’t know. Did the Lothal residents play 20-squares and senet? We don’t know. I also cannot tell you whether all of these pieces were found one at a time (such as the lonely Butrint piece, which was the kiss of death according to some chess historians because it could not be conclusively determined by other evidence that the Butrint piece was a chess piece) or whether some were found together. As some "experts" have said of the Butrint piece (it looks like a "finial"), these could all just be "finials."
It is tempting to assume that these pieces might be from a form of proto-chess. They were discovered, after all, in the area called Sindh (also called Hind in some 19th century literature on the subject of the origins of chess) and that is the area traditionally attributed by Murray as where chess first arose. I don’t know about you, but one of the Lothal pieces in the photo looks rather like a modern "knight" to me – very suggestive of a horse’s head. Rather like the Butrint piece looks like a modern "king" or "queen."