Honestly the game does lack depth to it. However it's not as much compared to what people originally think. (But it's still a considerable amount)
Lemme break things down. (For starters, I'll be using DMC4 mainly for comparison)
In DMC4, there are a whole list of advanced mechanics that actually deepen the gameplay. While some of these mechanics are kinda questionable and don't add too much in terms of combat, they create another layer of depth that increases the skill gap between a newcomer and a veteran DMC player. Not only this, but some techniques in DMC4 are incredibly hard to do due to the technical requirements needed to perform each technique.
However in DmC, there's not a lot of mechanics that the game has to offer that expands the combat system compared to DMC4. There are a lot of weapons that were added in DmC that gave the combat system more variety, but it still didn't give technical depth in the gameplay. And most of the mechanics that are in DmC are also in DMC4 or have been replaced with something different (E&I cancelling replacing DMC4's Guard Cancelling for certain moves). And when it comes to technical skill, I feel as if the game's difficulty of input execution comes from relearning the controls that DmC has, rather than actually pulling off complex maneuvers that require good execution.
When it comes to new mechanics, this is what DmC has to offer (from what I remember):
E&I (Ebony & Ivory) Cancelling: Equivalent to Guard Cancelling but with less uses. Cancels certain attacks with E&I (moves like Trillion Stabs and Prop Shreddar) This was also apparent in DMC3 and DMC4 but DmC enables you to certain moves much faster. It's not really a new mechanic
Reverse Rainstorm Double Jump Cancelling: Cancelling reverse rainstorm with a double jump to create an extremely short hop.
Gun Charge Stacking: Charging two guns at once.
Auto Gun Charge: Enabling you to charge guns without holding down the gun button.
Arbiter Drop Cancelling: Cancelling the start up animation of Drop by using it very close on the ground.
Rapid Slash Cancelling: Cancelling Vergil's Rapid slash with a jump
Doppelganger De-sync: De-syncing Vergil's doppelganger with charged moves
Airstand: Enabling you to attack in midair with a ground attack.
Airdodging: Being able to dodge in midair. Creates movement options.
From all of this, there's no actual depth to some of these mechanics since they don't offer that much when it comes expanding the combat system. The main thing that IS good is the Doppelganger De-sync and the Gun Charge Stacking since the De-sync can enable you to control both characters at once (similar to Ice Climbers in Smash Bros.) and with Gun Charge Stacking, you can use two charged shots in succession, creating some different setups. Not to mention that since older mechanics were taken out of DmC, this makes the game lack even more depth compared to what the originals had to offer. (Again, mainly talking about DMC4) I would also list the mechanics of DMC4 but that would kinda be too much since there's a lot to cover seeing how the metagame for it has been developing for years.
People aren't close minded for claiming DmC lacks depth. It actually does lack quite a bit of depth. And the people who actually analyze combat mechanics in various games can see it more easily compared to someone who's just getting into DmC for the first time without prior knowledge of the past DMC games.
Just wanted to shed light on this since a lot of people still think that DmC is superior to past games, when honestly it isn't.
Also long time no see to some of you. It's been awhile.