I think that the problem may be the other way around: it's hard to imagine his system because it's exactly the system that we're living under. There's United Nations lists 192 legal systems from which to choose. The only remaining question is whether this market is free. There's certainly outside regulatory pressure. Startups are a possibility (e.g. Tunsia, Libya), although there can be high barriers to entry (just like trying to move into the cable market). Not every country will grant you citizenship, but not every bank will loan you money. Leaving your nation can be difficult, but termination clauses are fairly common. Let me know if I'm missing something, but the market for legal systems would seem to be the least regulated market in existence.
It is actually insanely hard to change states, even if you take away all the human choice factors and pick a robotic subject that simply optimises for personal choice without regard to family, friends, ties to community etc.
All permanent migration is hard by design, some of it is harder than others, but even in the optimal case it's not easy. Further, although there may be 192 legal systems from which to choose, they simply are not that different at the end of the day in most ways.
The reason governments can afford to be so terribly inefficient is because they are the ultimate natural monopoly, and most people don't realise just how locked down they really are. When you actually make the decision to leave the nation of your birth and go some place else that suits you better it becomes abundantly clear that this is nowhere near as simple as it sounds.
I apologize if it came across unappreciative of the difficulties involved in emigration. Instead, I simply see the difficulties of migration being just as difficult under the author's proposed system. For the author's proposal, if we don't have a meta-legal system to prevent the various legal systems from trapping their customers, it seems that the new legal systems would use the same tactics that the governments use right now. It's so much easier than actually competing.
I guess it depends on the implementation details of the proposed system, the author is a libertarian (he talks at length of this in his other publications) so he may well have some very radical ideas on exactly how this could be accomplished, seasteading is the first that springs to mind, but I'm sure there are others.
It may also be simply an instance of order vendors so to speak, the government as the party with monopoly of force maintains a wholesale on order so to speak, but there are many many resellers within a market that expand on that based on various values and require their adherents to hold to various responsibilities in return for various rights, to greater or lesser extents.
If you could argue that this is a system which would extract more value from the governed population than the current one, then it does seem to be something of a self fulfilling prophecy that this ought eventually be implemented in some fashion. Of course, that's in question at any rate.