For me, when I am looking at Roguelikes, I also like to look at games that are INFLUENCED by the Roguelike genre. Diablo is undoubtedly inspired by the roguelike genre, in particular the first game which may not have a lot of the gameplay features of roguelikes, but the inspiration and THEME of the game are undoubtedly roguelike inspired. The theme of descending into a randomly/procedurally generated dungeon with a task that involves fighting and surviving your way down to the final level is a very clear roguelike theme.
While I wouldn't label Diablo and Diablo-clones (and I do say Diablo-clones and not ARPGs, because ARPGs could mean a lot of games that are NOT like Diablo) roguelikes, necessarily, for me my love of Diablo-clones comes from my love of Roguelikes, and the ways in which they are similar. So while I do agree that I wouldn't label them as roguelikes, I do NOT agree with the way most people seem to just dismiss the idea of there being any connection between the two, and refusing to discuss them. There is a huge connection there, and I think that history is important!