No, Google is under no legal obligation whatsoever to link to your site, let alone promote your site/topic using keyword autocompletion or instant searches. There's more to the legal definition of "anti-competitive behavior" than "anything that hurts someone else's business", although it's vague enough that I can understand the confusion.
Did you read the article? This is about autocompletion and automatic Google Instant searches, not removing anyone from the index. As with the huge list of terms that are currently "censored" (including every adult-oriented term they could think of), you just have to type the word without autocomplete and press enter to see the results.
In any case, suing the government for anti-competitive behavior doesn't really make any sense. Governments have much wider powers of regulation than businesses do, and for good reason. You could try a free speech lawsuit, but it'd depend on your country's free speech laws. One potential snag is that in the scenario you described, it's not really YOUR speech that's being restrained, but Google's.
