This shows a that the program linked is broken. The steps taken, are:

1. Animal House 2. ....

Going to the actual Kevin Bacon Wikipedia page, Animal House is clearly italic. The First non-italic, top-level (wrt parens) is Golden Globe

I expect the program is working off an out-of-date database. Hitting wikipedia directly would be rather bad form.

It took me 30 steps to do it manually, following the correct rules.

Haha ya, it's crazy. I went to Wikipeida.com, clicked on a random link (Ratko_Mladić), and from there it took me 26 clicks of first links to reach the Philosophy page.

When I first read the comic the other day, I went to the page in the comic (Spark Plug) and tried it -- didn't work, I ended up in a cycle between 3 math-related pages. Oops.

likely a result of subtle vandalism by other xkcd readers.

minor correction: 20 clicks

Three, actually. Kevin Bacon > Meme > Philosophy.

This statement shows a gross misunderstanding of the rules.

Meme is quite far down the page. It is well after many links that are neither italicized nor inside parens. The statement whose veracity is being checked says First link (plus some other parameters).