Gintoki is a lazy bastard, the only time we see him go out of his comfort zone, is when the people precious to him are threatened. And the level of effort he will put in also seems to be proportional to the amount of threat posed (like when the threat level is low, he will just save their ass while smiling smugly and stuff).
So, to convince Gintoki to put in all of his effort into preventing a future disaster like in the alt world, Gintoki needed to feel the sheer amount of suffering that would be caused if he failed; if he was just told some story, with a few videos; I doubt Gintoki would have risked his own life, as the story is just too damn far fetched.
A foreign virus that supposedly originated in the Joi war and stays dormant for 20 or so years, just to explode into the world, bombing it back to pre Amanto period? Yeah, is a very unconvincing story, unless you experience it, if you ask me.