Thanks Thomas, great explanation!
So I am a fool, a bit of at least 
As I woke up after some hours of sleep and analyzing the source code I also had a suspicion,
where my error was, but You made me see it clear.
Allow me to notice, that the sum of the first gradients is also not equal to zero.
The shift of 1 between both groups can be explained with logsoftmax(),
but what about nonzero sums?
Grads are orthogonal to [ 2 / 7, 4. / 7, 1 / 7 ]. And that is the point.
Prob manifold is a simplex, so the grads have to have zero sum of components,
to let me stay in the manifold.
What do you mean?