The Darkforce Dimension and the Dark Dimension have had long, separate histories in the comic books, they are not the same. They're not even related in the comic books in any way. Also, since established Darkforce users in the comic books such as Marcus Daniels (Blackout) and Tyrone Johnson (Cloak) have not only been introduced in the MCU but have also been established as Darkforce users therein as well, Darkforce in the MCU seems to be similar to how it is in the comic books and thus, most likely independent from the Dark Dimension in the MCU as well.
The most feasible way it could be a tie-in to Doctor Strange is by the virtue of the facts that Doctor Strange posited the existence of the multiverse in the MCU wherein one could tap into different dimensions as sources of exotic energies and that Darkforce is ultimately sourced from a different dimension only; namely the Darkforce Dimension. The Darkforce Dimension is where Darkforce users derive Darkforce from, most likely without the knowledge of said dimension.
After having invoked Dormammu, the zealots in the MCU, in addition to having become more powerful mages, have the ability to defy gravity and scale vertical surfaces, have the ability to create tangible blades of spacetime segments, have the ability to fold space and matter in the real world, and have the ability to resist time manipulation to an extent. It's most likely just the ability to resist time manipulation to an extent that manifests itself due to them being attuned to the Dark Dimension since we know that the Ancient One has also been attuned to the Dark Dimension but is only able to derive longevity from there and doesn't exhibit any of the zealots' other newfound abilities. These other abilities are obviously sourced from Dormammu himself, but for the sake of argument, let's assume that all these abilities come from solely being attuned to the Dark Dimension. In the second season of Agent Carter, it is revealed that Darkforce can send objects into the Darkforce Dimension, can make one invisible and inaudible indefinitely, and can allow one to open rifts to the Darkforce Dimension. In the first season of Agents of SHIELD, Marcus Daniels is revealed to have the ability to absorb all forms of energies and discharge said energy in the form of electricity or concussive Darkforce. In Cloak and Dagger, Cloak has the ability to generate and control darkness and shadow, and has the ability to teleport via movement through the Darkforce Dimension. None of the Darkforce abilities are a match for the abilities derived from the Dark Dimension.
While Darkforce is ultimately sourced from the Darkforce Dimension, one doesn't necessarily have to be a Darkforce wielder to be able to source it. It is possible to source it if you have the resources to and the know how, both in the MCU and the comic books. Darkforce has been known about in the MCU since the 1940s and is common knowledge, at least within the scientific community, to the extent that at least 2 agents in Agents of SHIELD were discussing it as trivia. It has been experimented upon significantly in the MCU; which is also the case in the comic books. A group of physicists were trying to harness it as a source of electricity, the research going wrong is what gave Marcus Daniels his abilities. In the comic books, characters such as Cloak and Mr. Negative got their abilities due to being subjected to experiments with Darkforce as well.
As for the Dark Dimension, nobody other than the Masters of the Mystic Arts know about it in the MCU thus far. This is also consistent with the comic books where only mages know about it for the most part, with the exception of a few characters who happen to know about it due to their association with said mages. The Dark Dimension doesn't provide any abilities in the comic books. With the exception of the Dark Dimension being beyond time in the MCU and thus, being attuned to it loosely disentangling you from the flow of time which manifests as longevity and limited resistance to time reversal, the MCU is largely consistent about this as well.
Given how they're significantly distinct in every medium, they don't even seem to be connected, let alone being one and the same. The only way that I can think of them ending up being the one and the same in the MCU is if they're retconned to be.