I generally wouldn't define algorithm as such, although I can see where the lines between them can become blurry.
Its pretty clear cut tbh. An algorithm is a set of steps to follow to produce some output. A trained model is, 'hey do these matrix multiplications with these coefficients to get an output'. The fact that the exact coefficients were arrived at via backprop, doesn't make it not an algorithm.
Indeed it is - for one thing, it allows us to see that various useful theorems and results about algorithms and computability apply as much to large programs as to small ones, such as the fact that there's no fundamental impediment to porting them between computers with different instruction sets, or running them in virtual machines.
What's not so well or usefully defined here is your distinction between hard and soft computing.
> In other words, a statistical algorithm does not point to the same category as a deterministic algorithm and an algorithm refer to the later class by default.
You appear to be under the misapprehension that the set of statistical algorithms is disjoint from that of deterministic algorithms. I strongly suspect that all the algorithms covered by the article are both statistical in terms of what they compute and deterministic in terms of how they do it.