When you say that the examples don't work, which ones don't work? When I go to the Documentation Center for DirichletDistribution the examples all seem to work as advertised.

Note that, for example,

DirichletDistribution[{1, 3, 2}]

is a symbolic representation of the DirichletDistribution at those values of its parameters. You need to then put it into, for example, PDF, to get its value at a particular point. So,

PDF[DirichletDistribution[{1, 3, 2}], {x, y}]

returns

Piecewise[{{60*(1 - x - y)*y^2, x > 0 && y > 0 && 1 - x - y > 0}}, 0]

And so on....

Read http://reference.wolfram.com/language/tutorial/ContinuousDistributions.html to get some more background on how to work with probability distributions in Mathematica.

When I asked about many-argument Dirichlet Distribution, I was told,

Neither multivariate distributions nor distributions with a variable number of parameters is supported in Wolfram|Alpha at the moment. Support for both are future goals.

I do not know of a Wolfram|Alpha language reference. It would be changing frequently.

If you have a question about what Wolfram|Alpha can handle, I suggest using the feedback slot at the bottom of Wolfram|Alpha pages (the slot enlarges when you type into it) or send email to info@wolframalpha.com.