You probably remember the scene in “The Godfather” in which Vito Corleone and the rest of the mob leaders meet to work out an acceptable truce in the ongoing war. Trump would probably view this as a template for his brand of politics: strong men (i.e., “winners”) ruthlessly pursuing their own interests by cutting favorable deals, with very little concern about the impacts to the public at large.
Unfortunately for him, the American political system doesn’t work that way. The Russian system, on the other hand, does. Hence at least part of his enthusiasm for Putin.