Intel's solution is cool, but it has some drawbacks ... one being that it's 720p max, the other is that it has that lossy compression to lower the necessary bandwidth (=> not crystal-perfect video quality).
Charging something via induction (electrostatic or magnetic), as previously stated, is something that has a very low efficiency due to the 3D nature of those fields, so you've got to keep the induction coil-thing as close as possible to the monitor, which sucks since if you wanted a fully wireless solution, you basically just moved the power wire from the monitor to the inductor. Oh, and you waste ≈5x times the energy.
Charging via a powerful LASER is also a possibility, and much more efficient (although this method has its drawbacks too).
Strapping a tractor battery to the monitor is also a possibility, my 23" screen uses about 30W max. A tractor battery is 24V and about 80Ah. Doing the math gives us a huge uptime, almost a week with a full charge for a normal PC user.