Oliver Dunne asks the exact question I had been wondering about myself: is it possible that any of Beckett’s games survive?
So far I have not found any. But I did find what may be the next best thing: a game between the two GHQ players Beckett played in the 1924-25 Armstrong Cup, Lieut. L. Mallin (whom Beckett beat in the first match) and Cmdt. L. Egan (whom Beckett lost to in the return match).
This game is from an Island Bridge Barracks v. GHQ second team match, played on February 22, 1924, so about a year before the Beckett games. It’s given in An t-Óglách, vol. 2, no. 5 (12 April 1924), p. 7.
The report says “criticism invited”. Well … while some of it is reasonable, there were passages that seem quite jarring today: the opening was odd, and in the diagrammed position White, to move, blundered with 25. Rd2??. After 25. … Be3 he could have resigned, but played on quite futilely for a while.
Of course Beckett beat the White player in this game (Mallin), and lost to Black (Egan). But the report goes on to say that Mallin beat Egan in two further games that evening. Make of that what you will!