The big nuclear war happens. Colleagues Dr. Wily and Dr. Light, knowing that their side lost the war, are playing games in the rubble, being the only ones left. Wily tries to rebuild the world as it was, via mass-producing cheap robots, while Light focuses on making a cyborg as close to human as he can. Being colleagues, they decide to have a friendly competition, and, to test whose plan is the better, pit their robots against each other.
Light's story about him building robots for peace and having them stolen by Wily was fabricated to convince Mega Man to fight. Which would explain why he gets released from jail and gets right back to making robots right after he gets defeated. ("I should have known Dr. Wily was behind this the whole time!")
But why are there newspapers being printed, covering Dr. Wily's arrest? Well, they were obviously printed by the two doctors, just throwing in random filler, including advertisements for a Cut Man video game, in the hopes Mega Man wouldn't notice.
But I don't know what all this means for the multiple spin-off series.
On popular demand, here's my favorite song from Mega Man 10.