Well, I figured that they were going for a parody of toy-anime in general and the resemblance to Beyblade in particular amused me to no end. As did the identity of the Tin Pin Tutorial Guy. XD
Well, it wasn't so much making fun of the characters' personalities as it was placing them all in an environment that was completely different from the original one they were in and see how it worked out. (Don't forget that all the characters in Another Day are alternate versions of the characters in the main story, they aren't the same people.)
By the way, have any of you all ever gone to Shibuya River during Another Day? Even if you don't read the secret reports, going there clears up a lot of things about exactly what's going on with Another Day.