Michel Thoby's webpage has the following formula for the equal-area projection:
r = 2 f sin(θ/2)
r is the distance from the centre in the projection plane of a point that is visible under angle
For 10 mm focal length this gives
r = 2 * 10 mm * sin(π/2 / 2) = 14 mm for the radius of the 180-degree image circle. This roughly matches the half diagonal of APS-C sensors (nominally 15 mm). Diagonal fisheye lenses using this projection indeed all have ~ 10 mm focal length (Nikon 10.5 mm, Sigma 10 mm, Tokina 10-17 mm).
The reverse formula for calculating the field of view will be
FoV = 2 θ = arcsin(r / (2f))
r is now the half-diagonal of the sensor. For APS-C with r = 15 mm and f = 17 mm this gives 105 degrees, which matches Tokina's claim for 100 degrees at 17 mm.
We can also make a plot to show the field of view versus focal length for equal area projection fisheyes, and compare with rectilinear lenses.
Most current APS-C cameras have slightly smaller sensors with diagonals closer to 14 mm, so in practice the angle of view will be a bit less than what's shown on this graph. Let's make another plot for the sensor size of an actual camera (Nikon D7100).
Note 1: This is not valid for all fisheye lenses. Some use different projections, such as the Samyang 8 mm, which is said to be closer to stereographic. The page linked above has a lot of information on various projections.
Note 2: Some projection software such as PanoTools use a more general projection formula of
r = k1 f sin(θ/k2) where
k2 are found empirically (from measurements) for different lenses. This page shows the results of such measurements.
Originally I made a mistake and forgot the one half factor from the sine function, which caused a wrong result and confused me. Instead of deleting the question I'm posting this as community wiki anyway as others may find it useful.