We introduce the notion of a weak A2 space (or just wA2-space), which generalises topological Ramsey spaces and countable vector spaces. Cano and Di Prisco introduced in 2023 the abstract Kastanas game on topological Ramsey spaces. I'll discuss how sets in a wA2 space with a determined Kastanas game, called Kastanas Ramsey sets, are related to Ramsey subsets of topological Ramsey spaces, coanalytic sets, and to strategically Ramsey sets (introduced by Rosendal) studied on countable vector spaces.