What is a "name/variable of base type" in applied $\pi$-calculus?
“Base type” is a type that isn't built from other types. Types built from other types include data structures (e.g. lists, arrays, pairs, …), functions, etc. In the context of the pi-calculus, base types exclude channel types.

Some typical example of base types in practice are integers, booleans, floating point, etc. From a theoretical point of view, a base type is one that is a base case in the type grammar, and more generally this implies that there's no type equation that relates this type with “interesting” constructed types. For example, a value of a base type is not a channel or anything that contains a channel.

“$n$ is name of base type” here means that $n$ is a channel that transports opaque values, as opposed to a channel that can transport a channel name. So $(\nu n.P)^{ch} \equiv \nu n.\mathsf{out}(ch, n).P^{ch}$ holds only when the output operation isn't extruding any of the channels in $P$.