Is this canon?

So far it is, until the games contradict it.
It matches perfectly with the games, even going as far as to show a few things such as Dante apparently reverting the shop back to Devil MAY Cry (as opposed to NEVER cry, as in the end of DMC1), or the first meeting and further collaboration between Trish and Lady (As well as showing kinda why she left DMC to work on her own). It also references somewhat the books when Dante goes back to "Tony Redgrave's" hometown.