There is, actually.
- The core of Dante's personality, keeping his cool in dangerous situations, has always been intact throughout the series as well as his basic appearance and personal arsenal.
- Then there's the fact that Sparda has always been the cause of practically everything that goes on in the games and that the major motivation for all the major protagonists, except Mundus, was to gain power.
- All the games have included the unsealing of demons, which is basically the core of everything that happens in each game.
- No matter what happens, Dante's the one that fixes everything. In DMC4's case, Nero ended everything, but it was Dante who had did the major job of destroying the Hell Gates as well as helping Nero out in his time of need.
- In all the games, except DMC4, there has always been a woman who Dante fights and ultimately ends up working with, basically DMC's equivalent to a "Bond Girl."
There's a few more I can list but I don't think I can type that much.
So, what makes DmC feel different to me?
- Even though DmC Dante still keeps his cool, his appearance and the design of his personal weapons are different so it feels like this Dante is just merely like the old one, making it feel like he doesn't exactly need to have the same name.
- Sparda's not the cause of what's going on in Limbo City, meaning that the very origin of DMC is gone.
- Limbo is ran by demons, so there's no sealing or unsealing to be done, meaning that Sparda never sealed the demons for anybody to unseal them and thus Dante can't clean up what his father left behind, the only thing that gave his objective substance.
- As stated above, Dante's objective has changed and, thus, his motivations have changed as well.
Basically, the motifs that had shaped the original franchise have either been gotten rid of or changed in the reboot.
Well I think you meant antagonists instead of protagonists.
Well Mundus's action were to gain political power because by killing Sparda, he was killing a symbol of hope in the demon world. I'm sure there were other demons who wanted to fight against Mundus and Sparda would inspire them to act. Killing him puts down the threat of rebellion or upsurper for a while.
On your second list, points 2,3,4 are assumptions and not proven to be true.
Plus sparda's history could still happen. He could still die or be out of the picture enough for demons to decide to take advantage of it. They decide to take over the human world using stealthier means hence Limbo's control over its populace.
Limbo could have been built on some demon's sealing site and after Sparda's dissapearance, some dude breaks the seal and Malice takes over. Think of what happened in 3. Either way Dante came to kick said guy's ass and reseal Malice.
Dante's primary objective was revenge on part of his mother so there is no reason to change that.