I consider the term requirements management to mean only the mainly mechanical administrative activities of capturing, categorizing, keeping track of and controlling changes to requirements. I see no reason why such activities would differ depending on whether or not it is a cloud-based application.
Another way to look at the question is whether there could be some differences between running the requirements management activities in the cloud as opposed to in a more traditional non-cloud environment. While each requirements management product has its own idiosyncrasies, I would be very surprised if running in the cloud would create any differences visible to the ordinary user. Of course, there could be impacts on those involved at a much deeper technological level, such as database and network specialists responsible for physically accessing and maintaining the cloud infrastructure.
If you consider that requirements management can include the requirements process, especially defining the requirements, then indeed there could be some requirements and definitional activities attributable to expecting the application to be cloud-based.
However, let me emphasize that whether or not the application is based in the cloud is entirely a design decision. Like all design aspects, though, basing the application in the cloud should be responsive to relevant requirements, which do need to be discovered. I fear that most of the time, using the cloud is what I call a buzzword requirement that needs to be satisfied even though those saying it's a requirement may have no idea what it means or why they need it. It's important that the cloud requirement be captured, but beyond that, any "cloud" will do.
A less cynical view would focus on identifying the value-achieving requirements for which the cloud turns out to be a suitable design solution to satisfy. Unfortunately, too often such requirements are defined so that they can justify the cloud design decision, rather than give a meaningful basis for coming up with it.
Typical requirements that might warrant a cloud-based design include supporting widespread access to the application and its data, accommodating (often unpredictable) increasingly large amounts of data to store, and avoiding responsibility for data center investment and operations. These are all types of requirements that should be identified regardless of whether or not one thinks the cloud will be involved.
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