There is no natural law regarding property rights, except to the extent that resources are indeed controlled and utilized by individuals. This however, does not imply that anyone has a right to those resources. I posit, then, that property rights are a social construct designed by societies in order to efficiently distribute scarce resources to its members.
For example, John may own a car. Carl wants John's car and has a key to it. It is within Carl's ability to take John's car for his own use. If John doesn't want Carl to take his car he relies on society, generally via the police force, to ensure that Carl does not take John's car.
Intellectual property rights are no different. We as a society have determined that intellectual property is property just the same as material property, and as such society sees fit to enforce the intellectual property rights. So, for example, if John owns the patent to a floor cleaning device and Carl tries to use that idea to develop his own floor cleaning device society will stop Carl from doing so.
If we have decided that intellectual property rights are worth having then we certainly need to enforce and protect them. Not enforcing intellectual property rights would result in that intellectual property's theft. Even now this is happening as video games, movies, and music get pirated daily because society does not have the means to regulate and control every connection between every computer. Without intellectual property rights' enforcement, there might as well not be intellectual property rights.
Of course, just because society has determined to enforce these rights does not necessarily indicate that enforcing these rights is beneficial for society. Economically speaking, intellectual property rights have their benefits and their detriments. Rights to intellectual help to foster innovation, as anyone who is interested in creating a new song, a new movie, or a new invention is assured that any economic gains to be made from their efforts will be made by them and not by others who only use their ideas. This makes the arts a profitable industry and makes innovating technology very desirable.
On the flip-side, intellectual property can make it very difficult for companies to grow or for new companies to enter an industry. Inability to utilize even basic ideas that have already been patented stunt the full growth of the computer industry, perhaps highlighted in the recent lawsuit Apple successfully filed against Samsung for using their patented technology in their tablet. Video game developers who might create amazing games about certain concepts or characters are halted from doing so by large video game copyright and trademark holders.
Intellectual property rights can be justified based on an economic argument. They can also be justified on principle, if you believe property rights are important. Certainly our society would be very different without them.