hmmm, if anyone cares to listen.... let's clear up some incorrect assumptions. While a lot of people had partially right answers. They were presented with some minor errors.
Wiiremote
Motion: The Motion control is related to ONLY the accelerometer inside the Wiiremote. The IR has no effect in the motion controls. There are 3 axis with the accelerometer. XYZ the same component judges both tilt and velocity. Which is why it's fidelity is good, but lacks the ability to track. As once velocity passes a certain amount the Tilt Axis value isn't in the data stream until velocity is slowed down. The MP are components to allow both Velocity and Tilt. The IR has 0 input in regards to the Motion control.
IR: The IR transmitted from the "Sensor Bar" is received by the Wiiremote. Having the Input on the user side allows for precise independent pointer. The 2 Points of the Transmitter allows for tracking distance of the points. The Wider the points the closer the remote. The closer the points the farther. It's parallax at work and something that anyone interested in the technology of these technologies should research on. This is Z depth tracking with precise accuracy because of the 2 HARD points of tracking. Though this tacking can only be done while the Wiiremote is facing the IR points. Which is a bit of a weakness as pointing away from the IR loses Z depth and Pointer. Also the 2 Points allows for a second Z rotation/yaw in the system that's not related to the Z Motion. Though to be clear the Pointer itself and the angle of of the Wiiremote/accelerometer has no influence over the pointer.
Move
Motion: Move Motion works on the same principles as the Wiiremote. It has accelerometer. It works pretty much exactly the same. It also doesn't need MP because...
Motion Tracking: The Move Camera uses Single Point tracking. The glowing ball. Which means that the Move can monitor what position the device is in at all times(as long as it can see the ball). It has a similar weakness to the Wiiremote IR, but because it's a BIG BALL it takes more intention to do so rather that just pointing our of angle as the Wiiremote. The Tracking doesn't require the MP or another 3 accelermeters, because the camera can do that instead. It can monitor the XYZ position & Velocity of the ball. Then determine orientation based on just the Tilt.
Pointer: I'm giving the Move it's own section on this though it's directly related to the Tracking. A single point transmission from the device SUCKS ass as a Pointer. It's a failure. Comes to Parallax again. How does move over come this shortcoming? The Eye get's XYZ position of the device then determines a "line" by knowing the Angles of the Move device. So the Move system requires both the Camera and the accelerometers to make a good pointer. This allows for a more harmonized(good) input rather than independent.(I worry that the unharmonized input of the Wiiremote is a penalty. one that will be proven or disprove with Skyward Sword)
The best thing any of you can do. Is "Do Your Own Research". Check out Parallax, Web camera input, wand input... there is a lot of input that's older and very relevant to the console techs. Don't assume. I've done my research and passed it on to you all. But I know that Fact is not something that many people like to hear. So do your own research that isn't from Sony, MS or Nintendo or other gaming websites. Get real research not bound by fanboy goggles.
So for the OP question. Yes it is massively required. Where as pure motion Wii games do not require the "IR Bar"
edit:
Well there has been some clarifications while I had SLOWLY typed my post. I think Nintendo should release a "new" sensor bar. That has a IR Points, Webcam and Wiispeak. I think Nintendo needs to copy this as it Moves towards community and good mass market ideas.