What oppression and persecutions do they get? They are the largest religion in the world! What do they want? A one world government?
In fact certain passages in the Quran have been widely interpreted to mean that it is the goal of Islam to be the dominant (or only) religion in the world. Also, there are many Muslims who cite the Quran to support their belief that government must be subservient to Islam. So yes, there are Muslims who believe that there should be a one world Islamic theocracy.
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As for the article in the OP, it's blatant chest-thumping. The use of violence by the Catholic church is mostly in the past, and the church has survived. All well and good.
The author (Alexander Lucie-Smith) compares Islam to the Catholic church: There is a violent aspect to Islam, just as there is to the Catholic church. However, that violent aspect of Catholicism has almost entirely ceased to exist. Those who promote violence in the name of Islam feel that their form of Islam is under threat. They sort of have a point, in that there may come a day when practically no Muslims use violence as an expression of their belief, just as has happened with Catholicism.
If and when that day comes, there will still be plenty of Muslims in the world, just as there are still many Catholics. The author says that "many suspect" that the continued existence of the Catholic church is due to its "proclamation of the truth and . . . the power of the Holy Spirit." They may suspect that, but a simpler explanation is that it's the result of cultural inertia, and the fact that many people find comfort in the teachings of the church. These same factors will ensure the survival of Islam even when it finally matures enough to almost entirely leave violence behind, just as has happened with Catholicism. The author more or less implies that he agrees with the violent Islamists who seem to think that without violence, Islam would whither away. They're both full of shit.
ETA: I found the article from the National Secular Society
that Lucie-Smith linked to be more interesting, but also problematic. I don't see a "de facto blasphemy law" at work, rather a willingness on the part of certain non-Muslim elements in society to buy into an Islamist narrative.