Hardly a farce of 'Jobsian' proportions, just common sense
I don't think it's silly at all for Apple to try to trademark App Store. They have put time, energy, labour, advertising, etc. all amounting to hundreds of millions of bucks worth of investment into the whole App Store idea. The name is part of that investment. Of course they want to protect it.
The article mentions two arguments against the possible trademark.
1) Apple wasn't the first to use the term. That may be so, but Apple are the first to use the name to market their products and file for trademark. That counts, not the first incidental use of the term. Properiatary rights in relation to trademarks are aquired through use in the market place and/or through trademark filing. No one else has done that before Apple
2) The term is generic and just describes the product. That would be true if they had called it Application Store or Software Outlet. App is not only an abbreviation of Application but obviously also a play on the word Apple.
I doubt they will be able to prevent anyone describing their software shop as 'an app store', but I would think they stand a good change of preventing others calling their outlet 'App Store', and that's what this is about, and it sounds pretty fair to me. If I started business in some sort of small and crude wooden building where I would sell pizzas, I might get away with writing something like 'come to our pizza hut', but I doubt that anyone would think it fair that I put a sign over the door saying 'Pizza Hut'. No?