According to The Wall Street Journal, ESPN and Univision have been sending take-down notices for short clips or compilations of World Cup highlights. Vine, which is owned by Twitter and allows users to make six-second videos, has suspended at least two accounts as a result of complaints by Univision. Slate.com has taken down an eight-minute compilation of all of the goals scored in the World Cup due to a complaint from ESPN (who says it is helping FIFA out).
The Wall Street Journal article gives a nod to Fair Use, but doesn't delve into it. There's little doubt FIFA and its licensees have the right to control broadcasts of the World Cup performances, but at least in the U.S. there are Fair Use issues, and also First Amendment/Freedom of the Press issues to consider. Six-second Vine videos seems as good a candidate for Fair Use as anything, frankly.
As for the press? FIFA says they make exceptions for bona fide news purposes - subject to the media outlets signing a news license agreement. That's a First Amendment problem, in my view.
What works most in FIFA's favor on the Vine issue is that people posting Vine videos aren't likely to challenge these actions in court. If you have a six-second fan video taken down as a result of a DMCA take-down notice, are you likely to file a counter-notice and invite the rights-owner to sue you? Are you likely to state, under penalty of perjury, that you have a good faith belief that you are engaging in Fair Use (keep in mind Fair Use determinations are complicated, and require analysis of a variety of factors). There is little to no push-back from makers of these videos.
As for Twitter and similar service providers, when they received a completed take-down notice, the accused videos are coming down, period.
As an IP attorney, I'm all for content owners protecting their rights, and I'm going to come down against those who want to see the IP system dismantled entirely, or who constantly argue against content creators. Keep in mind, however, that the copyright system was established with specific goals in mind, and depends on a healthy balance between the rights of authors and public benefit. It is not just a system for content creators and/or rights holders. Tipping the balance too far in the wrong direction undermines public confidence in the system.