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Always check the definitions being used in the reference - there are even slight differences between HAG2 and Toen's global overview. Once you know you have an epimorphism from a union of affines, saying that $X$ is $n$-geometric in the HAG2 sense basically amounts to saying that the higher diagonal $$ X \to \mathrm{map}(S^{n},X) $$ is affine. Thus $0$-geometric is equivalent to semi-separated, and any algebraic space $X$ is $1$-geometric because $\mathrm{map}(S^1,X)\cong X$.