1... maatorc, The Journal of Parapsychology defines paranormal as "any phenomenon that in one or more respects exceeds the limits of what is deemed physically possible according to current scientific assumptions". Not only it does not follow from this definition that the paranormal cannot exist, but this definition does not come from skeptics, but quite on the contrary, from the other party.
2... It is not Randi who says, "I deem some stuff that rarely happens in nature paranormal and I challenge you to prove it". That's a gross misrepresentation of the situation. It's the people out there who claim that they can predict future by the use of astrology, tarot cards, or contact with spirits. It's people out there who claim that they can use extra-sensory perception to gain access to obscured information, that they can use simple tools to locate hidden items such as water or metals, that they can heal serious diseases of other people by touching them. It's them who claim they have these powers and it's them, their peers and believers, who call these alleged powers paranormal. It's them who claim they are rare but ubiquitous. It's them who are so confident in these powers that they will charge money to provide that kind of service.
3... What Randi says is, "if all of this is true, if you claim that your claimed powers do work, if you are willing to sell them to others based on that claim, then come and show me with a trivial demonstration of your choice that they do work; I'll give you a million dollars for that". And their reply? Silence. The obvious conclusion? They are all full of [rule 8].
4... This has nothing to do with scientific research. And everything to do with challenging false claims that frauds out there make.