You can perform element-wise multiplication and then sum along the second axis, like so -
C = (A*B).sum(1)
These multiplication and summation operations can be implemented in one go with np.einsum, like so -
C = np.einsum('ij,ij->i',A,B)
With np.matmul/@-operator
-
(A[:,None,:] @ B[...,None]).ravel()