Well, electronics is my strong point so maybe I can take a stab at the issues.
The LEDs have a 3-3.6V "forward voltage". That means that at the rated current, the voltage across the LED will be 3-3.6V. It does not mean you can put 3.6V across it and expect it to survive. Unlike most electrical and electronic devices where the supply (battery, line voltage, generator, etc) decides the voltage, and the load (Lamp, radio, heater, etc) will pull some amount of current at that voltage, the LED wants to decide the voltage, and the supply has to decide the current. But the battery is crappy at deciding current. It wants to supply voltage. That's where the driver comes in. The driver turns the voltage source (battery) into a current source that the LED wants.
The output of the driver is connected to the LED, so we need to make sure the driver's output characteristics are suitable for the LED. The driver's input is connected to the battery, so the driver's input characteristics need to be matched to the battery.
The primary output characteristic of the driver is the maximum current. In this case it's 1.05A. The LED has a max current of 1000mA, or 1.00A. If I was being fussy, I'd say that these are incompatible, because the driver can supply too much current to the LED. If I was designing a product that had to run a lot and last a long time, I wouldn't do this. But in the modding world, Crees are often overdriven much more than this. The consequence is that you have to be really careful with heatsinking, and you can't expect a normal lifetime on the LED. If you are going to do a good job with the heatsinking, I'd say go ahead. Otherwise choose a lower-current driver.
The secondary output characteristic of the driver is the allowable voltage range. This is not always easy to find, but I know that driver is based on AMC7135 chips, and that the '7135 has an allowable output voltage (remember, the LED will be choosing the voltage) of zero to about 0.15V less than the input voltage. When the battery is fully charged, (about 4.0V on load), this translates to 0-3.85V, and the LED voltage is within this range, so we're golden. When the battery is discharged (3.0V, give or take depending on your battery and your preferences), the output range of the driver is 0-2.85V. Uh-oh. This means that at some point during the discharge, the driver won't be able to shove that 1.05A through the LED any more. The light isn't going to suddenly go out, but the current (and therefore the light output) will start dropping. I think with these components it would continue to drop all the way to zero. Some drivers will suddenly shut off at some point, but I don't think this one would.
The input characteristic of the driver is it's allowable voltage range (the battery will be determining the actual voltage). This driver says 3.0-4.5V. That fits well with our battery. This assumes you use a typical "3.7V" lithium-ion rechargeable battery. Other lithium batteries are lower voltage and so not well suited to these components.