When they meet Findlay says he's heard Eddie plays pocket billiards (i.e. pool) and then asks him over to play billiards, so I think Eddie and Bert assumed he was still talking about pool. And later Findlay says he does play pool, just not at home. Still, I agree that Bert should have worked that out ahead of time.

Extremely odd. Bert wouldn't have let Eddie play. Bert would have set up the game long before they arrived. Hustlers don't like surprises.
Hey, Bert, bet your money on a game I've never played. Sure, Eddie, but I won't be betting on a sucker.
Mairzy doats and dozy doats, but liddle lamzi nothing.

Yeah. A little odd. But around here the terms pool and billiards are more or less synonymous. The term pocket billiards (pool) is not used much. Somebody could have told Gordon long ago that Findley was a billiards player, and Bert just assumed he was talking about pool.
In any case. Didn't impact the quality of the film one iota. A classic, through and through.