This is very close to how I would render it, with two small caveats.  I phrase my function docstrings as imperatives (analogous to Git commits); thus "Construct..." instead of "Constructs."  This again helps to keep things terse, and there's a general preference for it in the community.  I'd also suggest we drop the code face from "key", and then of course correct the grammar.

Also one small nit.  __init__ doesn't technically construct an object -- that's the job of __new__; __init__'s duty is to assign initial values to the object.

All this said, I'd recommend something like the following: "Initialize the client for use with the given KISSmetrics API key."  Or something along those lines at least.