Here's the result. Yup, www.wolframalpha.com is in there, but most of the way down the page.
Google, by contrast, has it as the first result, exactly as one would expect.
Meanwhile, Wolfram Alpha itself isn't sure what to do with "wolfram alpha search engine" as a query, and suggests I try "wolfram alpha". And then tells me it's too busy. (This isn't part of what I'm referring to in my subject line; I know it's not trying to do the same thing as Google. Nonetheless, if this were Google, it would (a) have given me actual snippets of information about the possibilities it came up with, not just suggestions for things to try, even if it didn't recognize that "search engine" was an extraneous modifier on "wolfram alpha", and (b) would not have been too busy.)
Meanwhile, for your amusement (and where I came across that Google ad in the first place): The Wolfram's Beta computizzled knowledge engine.