I think that the existing implementation of the idea and where it has lead has numerous problems, but the fact of the matter is that it is beneficial for a society to have mechanisms like patents in place.
The article argues that things would still be done, which is true, but in the case of inventions, the problem is that they wouldn't be shared and companies would probably work hard to obscure any innovations that they did make to make it harder for competitors to copy them.
The argument for getting rid of trademarks is also kinda weak. The end user should be able to easily understand what it is they are buying. You shouldn't have to worry that some sneaky guy is selling cow manure in a box and calling it cheerios.
Beyond that, the point that removing IP restrictions everywhere else would only have a positive effect is something that I tend to agree with.