Your observation is correct that the Spine Outline shaders are behaving like a stroke effect and not like an outer glow effect in terms of a gradient falloff.
Unfortunately the implementation of all Spine Outline shaders is based on sampling the surrounding 8 pixels to see whether solid pixels are nearby or not. To make the outline smoothly transparent near opaque corners, a lower number of opaque neighbouring pixels leads to a more transparent outline pixel, similar to anti-aliasing. The shaders could theoretically be modified to show a linear falloff, that would require a loop of N instead of 1 iterations of sampling these surrounding 8 pixels, with growing distance. This would be rather costly in terms of fragment shader computation time however, so it depends on how many of your skeletons require this shader active at the same time. The respective common shader code can be found in Spine-Outline-Common.cginc:Line30, if you really would like to go down that road.
Another approach, which is not as costly performance-wise, would be to create an additional distance field atlas texture (or encode it in the alpha channel) where every pixel's color value is set to the distance to the closest opaque pixel. This could be done in Photoshop (you could simply use the outer glow effect) or you could write a script that generates such a distance-field texture programmatically in Unity, whatever you prefer. You would then need to write your own shader similar to the outline shaders which evaluates this distance field texture and outputs the opacity based on your respective settings.
A completely different approach would be to use a post-processing effect for the glow effect. You should be able to find such effect packages on the Unity Asset Store.
