If the environment contains the simultaneous presence of two or more players, it is contemporal. If not, it is atemporal. Games can combine both contemporal and atemporal play, though not at the same time. Temporany is a property of real time rather than game time.
Temporany is also different from concurrency.
The description of games as synchronous or asynchronous is often used casually to mean games where players are present in the same space, or not. It is not correct because simply being in the same area as another player does nothing to explain whether or not you need to be in sync with his game or not.
What Games Are solves this confusion by splitting it into two terms: synchrony (which describes whether play needs to be in sync between players regardless of time) and temporany (which describes whether play needs to occur in the same space and time regardless of sync).