Why does the Eurofighter Typhoon pitch up on brake release? In the video here of an airshow take-off, it's noticeable that when the brakes are released there's a brief but pronounced fluctuation in pitch as the aircraft accelerates. 

This is something you see in very fast accelerating cars / dragsters, but I believe that is caused by the torque through the rear wheels, which is obviously not the cause here.

The same thing can be seen on an F-16 but much less pronounced.

Certainly for the Typhoon, the nose-wheel oleo doesn't seem to be particularly compressed as it's held under braking. I'd guess that you want to ensure that there's no chance even the slightest bit of any upward vector in the engine thrust while you sit on the tarmac, otherwise your brakes might not work, but that doesn't really explain the wobbling.

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When the brakes are on, they apply a backwards force that counters the engine thrust. This force is applied at ground level, and the engine thrust is higher. These two forces result in a moment that forces the nose down, compressing the nose gear slightly.

When the brakes are released, the moment disappears and the nose gear extends.

Another factor here is that the Eurofighter (and F-16) has its air-intake under the fuselage, which forces the designer to put the nose gear behind the intake, closer to the main wheels than other aircraft. That means the nose gear has a shorter lever-arm to resist pitching. It's set up with the same spring rates and damping because it's primary job is to react to bumps in the ground, so it's more sensitive to pitching.