It's not clear to me why the author should be bound by terms of service that he never agreed to.
A web request is merely a communication with the web server. The server is free to do what it wills with such a request. If Wolfram doesn't want to respond to requests from the author's apps, that's well within their rights. Similarly if they do respond, it's because they explicitly set it up to so respond.
You read every ToS for every service/product you use?
Community and social standards often trump legalese. For instance, most absurd restrictions in apartment rental agreements are not enforceable.
In this case, linking to another site, no matter how "deep" the link is, is common practice.
If WA really doesn't like it, they can prevent it by checking the referrer, or going even further by adding a pseudorandom token to their query page, switched every 5 minutes and valid for an hour or a day, and redirecting deep links which don't have a valid token.
Of course, doing that would probably kill some traffic they like, so they have a silly, selectively-enforced and probably unenforceable ToS clause instead.
I don't see any reason why such provisions need to be enforced legally, since they can be enforced technologically in most cases. Expanding the law because of laziness is a horrible precedent.
I find it amusing that people downvote my comment. I guess it is much more rewarding to upvote overinflated stories about how Evil Wolfram Alpha "Doesn't Get It" (often without reading the story, I suspect). Makes for better drama.
Frankly, I would much rather read about a 2-bit adder implemented using 36 555 timers.
A web request is merely a communication with the web server. The server is free to do what it wills with such a request. If Wolfram doesn't want to respond to requests from the author's apps, that's well within their rights. Similarly if they do respond, it's because they explicitly set it up to so respond.