The client api you referred to is for use in JS actions/JS snippets, for pluggable widgets refer to The pluggable widget api
If you let us know what you're trying to achieve, we might be able to point you in the right direction
You might have to implement ListActionValue API
I don't know anything about your usecase but have you considered using a JS action instead?
Even though the answer is already accepted; it IS possible to load the client API inside a Pluggable widget. There are use cases for widgets where this is needed as I needed to do this in the past several times as well.
Why do you think you need the client API?