On the Wikipedia page for 9/11 where it lists various international responses, it is mostly an outpouring of support. However the section ends with some Greek soccer fans trying to burn an American flag. Was this hooliganism, or a sign of some broader antipathy toward the US in Greece at the time?

Not a historian and not Greek

I was able to find an article that deals with the same topic but it's by the Guardian which is a British news media source

From the article[1]

leftwing groups and labour organisations will gather in front of the neo-classical facade of Athens University for a rally "against war"

The match involved AEK Athens, who according to the Morning Star (they were formerly linked to the Communist Party of Great Britain), have left leaning sympathies[2].

According to a student, it was a case of [1]

"What goes round, comes round,"

"A lot of people died and that's a pity, but the Americans are getting a taste of what they did in Korea, Vietnam, Cambodia and the like."

A bit of it originates from perceived American inaction in the situation in Cyprus [1].

Among the many ills that Greeks cite is America's failure to pressure some 35,000 Turkish troops to withdraw from Cyprus, 27 years after Ankara invaded and seized the island's northern third in response to an Athens-inspired coup.

That failure, they snort, is a perfect example of "American double standards". The reaction is mirrored in Cyprus, where one in four Greek Cypriots told the Politis newspaper last weekend that the Americans "deserved" to be targeted.

According to Morning Star, AEK Athens who's fans were involved in the incident, have their origins among the refugees who left modern-day Istanbul after the Greeko-Turkish War [2], and given the Turkish involvement in the conflict in Cyprus, this too potentially played a role. [2]

The crowd there based on another incident in the same match, looks highly enthusiastic with fans climbing over fencing and firing flares later during the same match after the incident

In a very oversimplified manner, basing my opinion on the scholarship of the Guardian article, due to some reasons, some sections of Greek society who also happen to be fans of AEK have a certain level of dislike for Americans which led to them reacting positively to the incident, which finally led to the incident in question

Sources:-

[1] The Greek approach to tragedy | World news | The Guardian

[2] Men’s Football Leftist clubs around the world | Morning Star (morningstaronline.co.uk)

/r/AskHistorians Thread