MissScarlett: The games (there was a companion, colours reversed, running concurrently) can be followed through the chess column of the <Bombay Gazette>.
The August 20th, 1851 number announces:
Between the Chess Club of the First Bombay European Fusiliers (at Poona) and certain Bombay Players.>
Game 1 (this one) has <1. P. to K4 P. to K4> whilst Game 2 has only <1. P. to K4>
By August 25th, a pair of extra moves are recorded. And so it continues periodically through into 1852 (I haven't sought to check every column); by February 25th, Game 1 is as far as <33. P. to Kt4>, whilst in Game 2, Poona - as Black - has reached <28. R to B5>.
There the trail apparently goes cold - maybe the columnist lost regular contact - but apart from one more update on May 18th (Game 1 has progressed to move 47, and a Game 3 has begun, reaching move 7), I find nothing more until February 23rd 1853:
<We give below the first game in the late contest between the Chess Club of the First Bombay European Fusiliers, then stationed at Poona, and certain Bombay Players. Apropos to this match, we have received the following letter:
<Camp Colobah, 21st February, 1853.
Sir, - Having observed in the Gazette an intimation that you intend republishing the Games played between our Club and certain Bombay players, I beg to inform you, that, owing to our best players having proceeded to Aden with the Right Wing of the Regiment, we are reluctantly compelled to relinquish the contest. Our Club, though divided, is still maintained in the Regiment, and we shall always feel happy to aid, as far as we can, your laudable efforts to promote the noble Game of Chess.
I am, Sir, your's truly, PHIL. [?] HEATON, Secretary, Chess Club, 1st Fusiliers.>>
This game is then given in its entirety, with light notes.