I think thats a pretty big oversimplification and a faulty definition of both the Dictatorship of the Proletariat and of Anarcho-syndicalism. If you had said that the classless society would have come about after the DoP, I would have agreed, but since you didnt, I have to differ.
The DoP, I think, is simply the working class taking control over the means of production and subsequently the power. Instead of the Dictatorship of the Bourgoisie, we have the DoP, and I think this is applicable to all of the revolutionary socialist theories there are. Every one of them argues for the working class to take control over the society.
When it comes to anarcho-syndicalism, and the state of society organized after its lines, I think youre either forgetting or leaving out big chunks of the ideology (if I can call it that). A society organised with the revolutionary union as its basis, which is what syndicalism strives for (at least as a transition), is very different from what the communists believe.