I'm about half way through... but I'm not sure what you're stabbing at? He seems to be just making the argument that virtual property need laws to protect them? I'll have to finish it later though.
I think it really breaks down about how far you simply want to take the 'property' argument.
Are bitcoins property in the eyes of webster's? Yes
Are bitcoins property in the eyes of the law? I'd say in many cases yes.
Are bitcoins property treated the same way your car is? Ok now you're going to run into trouble. This is where the author of the paper seems to want to take things.
The paper establishes a scientific basis on what characteristics a virtual property must possess to be "comparable" to properties in the common sense. One of them is rivalrous, i.e. the CAPACITY for it to be restricted to one person only. This is provided by the bitcoin network, because an unspent output can be protected by secret keys, for an indefinite time (persistence...).
E.g. a music file CAN NOT be virtual property on that basis, because once it's copied you loose control over who has access, so you can not establish rivalrousness. Thats why you need a different legal handle to protect artistic content.
Rarely is the law scientific about anything

But I guess my point was that he's just making an argument... He isn't talking about what they are he's talking about what it should be.
I would say I agree with him in general; though one can poke holes in most arguments. Like for example he didn't mention value. This doesn't matter in the real world because everything no matter how trivial is still 'something' but a computer can generate digital property like crazy. If I fork the blockchain and create 'reyalscoins' do they really deserve legal protection even if I'm the only one that uses them? (you're free to use them if you want so they'd still have 'interconnectivity')
But has anyone here actually stake out the position that they're not property? The real argument would seem to be more what laws that apply to 'normal property' as written really apply to bitcoins. But each one of those topics could occupy an entire thread itself. Inheritance tax for example could spawn several pages of back and forth.
I agree that he is making an argument, but in order define a previously undefined phrase that definition must be proven.
As far as value, VP is a general term to encompass Domain names, URLs, Bitcoins, etc. The definition of the general term should not hinder the value of anything specific that falls under it's scope.
If we were trying to define Bitcoins would you want to hinder the value by definition or allow the free market to determine that value.?