Firstly, 'property' is not a clearly defined concept. It has a series of features, which may not be present in all types of property. For instance, I might own real property which my local authorities put conditions on, forbidding me from building anything above three stories, or requiring a building permit before commencing works. Nobody would suggest that this is not my property though.
So what is property? Property at its core involves society granting one or more 'property rights' in respect of an object. Those property rights are all monopolies over certain things, such as a monopoly over possession, a monopoly over any profits etc etc. Each one of these rights can be individually cut off and assigned to a third party, or temporarily licensed to someone.
Which brings us to intellectual property, or more specifically in this instance, copyright. Copyright too is a grant of a series of monopolies rather than a single monopoly. The right to reproduce, the right to create derivative works etc are what is termed 'the exclusive rights' of copyright owners. What this article is describing is the exercise of those rights. Yes, when you purchase a DVD, you are not purchasing the underlying property. If you were, then you would be getting the film company's rights (which they may have spent hundreds of millions of dollars creating) for the very low price of $19.99 (or whatever you happened to pay for the DVD). Because they are granting you a licence, you get a limited licence for a fee.
If you don't like it, contact them directly and arrange terms of a different licence for a different fee. They have the power to do this because they own the property, not you. You might think you own the property but if you think harder about it, you own the physical DVD with its copy of the film, not the right to make unlimited copies of the film itself (which would amount to you owning the film, which is ridiculous).
The problem with Hollywood has nothing to do with some sort of fundamental flaw in the nature of copyright itself that we have failed to spot - it has to do with the failings of Hollywood to build a distribution model for the digital age that uses an online intermediary as a means of protecting property rights rather than suing individuals in a bid to make an example of people. It has to do with the fact that as Larry Lessig said, in the modern era, code is law - the software we create to protect things is more important than the laws we use to do so. The fact that it took so long for Netflix and Spotify to build businesses is proof of the fact that the code here hasn't kept pace with the law - if it had, we wouldn't have this problem. If the RIAA spent half their lobbying budget funding innovative new startups, they would have saved themselves a ton of money and we wouldn't be having this discussion.