When you consider that the current Egyptian regime bases much of its legitimacy on the struggle against colonialism, this notion that it really plays the role of quasi-imperial agent seems striking, though of course many within the Arab world would take it for granted in their own political worldview. The reasons for this are not entirely political - this is not the old extraterritoriality of the unequal treaties - but rather economic. If Westerners with all our economic power stopped going to Egypt, it would devastate their economy. Terrorists know this, and it is one reason they attack tourists, whether in the Sinai or in Cairo itself.
The United States is obviously not the Roman Empire in the sense of conquering and annexing territory, but then the Aztecs did not formally rule much of central Mexico, and their dominion is still often called the "Aztec Empire." "Empire" is not a concept handed down from heaven, but one we invent to describe various similar phenomena in the human experience, and as such we can consider it wherever it might be useful. Are Americans imperialist colonizers out to conquer and loot the planet? Not generally. But when currency and many streets and buildings in Egypt have both Arabic and English labelling, when there is an entire security service the public face of which is primarily the protection of largely Western tourists, when the premiere institute of higher education is "American University," and when the Egyptian government tries to control many gatherings of its own people while protecting an embassy-sponsored Fourth of July celebration, there are definitely elements of an imperial hegemony in play.