I think that's true in many respects, but unfortunately Dalrymple's point isn't very clear. He wanders from his initial point (a country adapting its laws to the laws brought by immigrants) to another point, which is the responsibility of the immigrant to assimilate (into a nation, which as you point out, is now no longer a concept that has much meaning to many people).
I think a nation still must enforce its laws on anyone who happens to be within its purview: any immigrant, any person who has committed a crime within its borders, etc. I would have been happier if he had made the point that a country must still stay with its own legal structure, regardless of the attitude of the immigrant.
Our post-national cities, New York and Miami (particularly the latter), have populations that in general come from countries formed in the Greco-Roman/Judeo-Christian legal tradition of the West. They might have different cultural approaches, and they might need encouragement to learn English, but basically, the law is the same.
I think the problem is that London is receiving a large number of immigrants who don't come from this tradition or anything like it, and is making the situation worse by adapting to their legal system rather than making them adapt to its.
Agreed, the biggest threat the the Western way of life and our legal and cultural traditions lie not in the Chinese investor or the Mexican laborer, but in the Muslims of all classes and ethnicities who seek to force us to accept sharia little by little, and then complain about "discrimination" when they don't get there way.
In Italy and in Spain, you have large populations of folks from the Andean countries (Ecuador and Peru especially) who, despite their racially mixed heritage and cultural idiosyncracies, don't seek to force their host societies for "special accomodation", nor do they exhibit hostility toward the majority (the national group with the second highest rate of intermarriage with Italians are the Peruvians, Albanian Christians being first, interestingly enough). This is NOT true of the Muslims, although secular Arabs are not much of a problem (and often came to Europe to get AWAY from their "traditions").