Thanks for catching that documentation bug 
, @sbslee!
And sorry! That must have been frustrating. We undertook a major reorganization of q2-diversity during the last two release cycles (2020.6, 2020.8), during which alpha, beta, and their phylogenetic counterparts were refactored as pipelines. This failure to update the docs slipped through.
If you run into this again, here's a trick. In QIIME 2, there are three types of Actions: Methods, Pipelines, and Visualizers. (They all subclass Action, if you're familiar with object-oriented programming concepts).
If you're not sure which type of Action the command you want is, the API should let you use the more-general <plugin>.action.<command> syntax in place of, say, <plugin>.methods.<command>. @Nicholas_Bokulich's example above does exactly that:
If you're using tab-complete, it's usually easier to find what you're looking for if you use the right type:
... but you'll notice that alpha shows up alongside everything else in the complete list of Actions:
Thanks again for calling this to our attention! I'll fix it ASAP.
Chris 
EDIT: This issue will be fixed here.