(NB: Americans, since your author is one of those damned Britishers, take 'football' to mean 'soccer' here, not the rugby-on-steroids game with all the padding.)
If I said football violence to you, possibly you'd think of hordes of angry tattooed British men storming the pitch and throwing things at each other. Millwall bricks and all that. This, however, is Conference League stuff compared to what goes on elsewhere. A few hundred drunken Liverpool fans going on holiday and boxing with the local riot police pales in comparison to, for instance, starting an actual war.
Which has happened. In 1969, El Salvador invaded Honduras during the qualifying round of the 1970 World Cup - actually, in their last match, El Salvador won 3-0 anyway, demonstrating a thorough knowledge of the 'crush your enemies into the ground by any means necessary, even when you're almost certain to win anyway' school of thought. Granted, the actual causes of the Football War were a lot more mundane; immigration and land ownership, mostly; but football provided an easy flashpoint for nationalism, and a little bit of hooliganism was always going to inflame the situation.
Probably the most stark set of examples, however, come from Eastern Europe, where football hooligans mostly took the form of ultras, fanatical, violent supporters with a lot of ties to fringe politics, mostly on the right. The thing about football, as Terry Pratchett put it, is that it's not about football. Plenty of sectarianism and other such unpleasant history gets worked out on the terraces - even nationally, England seem terminally unable to shut up about the war whenever they're playing Germany. But where most of the time football matches happen because of old wars, in the former Yugoslavia you can trace a bit of a war happening because of old football matches. The ultras of Red Star Belgrade, a Serbian team, formed the nexus of a paramilitary unit called the Serb Volunteer Guard (more commonly known as Arkan's Tigers). Their history of involvement with ethnic cleansing and genocide is fairly well-known, if on the minor side compared to the bigger parties involved.
But the point is that football provides an easy link to nationalism in situations where that would be difficult or impossible - the Palestinian diaspora in Jordan almost universally support a team called Wahdat, which is named after one of the larger refugee camps there. Back in the Balkans again, there's a story about Croatian soldiers at the start of the war using the Dynamo Zagreb crest on uniforms and vehicles, not having a flag readily available. Some of Zagreb's ultras got used as an irregular force on their side, additionally.
Which brings me to Egypt. One of the more obscure pieces of news to have come out of the country since the protests against Mubarak started in earnest was that a lot of the initial organisation came from football supporters' clubs. And there's a number of reasons why that might be. Certainly in an authoritarian regime in the Middle East, secular or not, football and Islam are two of the (limited number of) things it's possible to get genuinely angry about without the government breathing down your neck. The fact that these groups are mostly comprised of young men with a unifying cause and some level of organisation that's beyond the state's control makes them a genuine threat to repressive regimes, when they can't use them to their own ends.
Incidentally, football stadiums themselves are a favourite venue for public executions, having been used by (amongst others) China for shooting condemned criminals, Afghanistan under the Taliban for stoning women accused of adultery to death, and Rwanda during the genocide there in 1994, with about 8,000 people in all being murdered at Kibuye and Gatwaro stadiums. North Korea uses them for show trials, when they aren't putting on gigantic displays of hivemind Juche choreography.
But what's the point of all these datapoints? If nothing else, they demonstrate mankind's propensity to tribalism. 'Us over here in the blue shirts are the good guys, those guys over there in the red shirts are bastards', if you like. Football, like anything else in life with that much emotion invested in it, can be as powerful a dividing force as a unifying one.
So don't get into an argument about the offside rule. You never know where it might end up.