Terminology is going to be critical going forward, a perpetual problem with different organisations using different terms for the same thing and the same term for different things. The article confronts this early on, questioning the use of grant identifier. However, it then proceeds to use the term grant identifier throughout, even when referring to an application for a grant. The way in which research is funded is changing, and grants are being replaced by other funding mechanisms. Therefore, we need to stop using the term grant as soon as possible.
From a funder perspective, someone who is requesting funding generally submits an application. If the application meets the funding criteria, which may be objective and/or subjective, then is can be awarded, possibly in the form of a grant. It is wrong to apply a grant identifier to an application, because it is not a grant at that point.
I suggest the term used is Research Funding Identifier. This works for different funding mechanisms - grants, loads, fellowships etc, as they are all types of funding. It also works for applications as the term does not presuppose that funding has actually been awarded. Potentially, the Research word could be dropped, since not all funding provided by the funders is for research. This would give the term Funding Identifier, which is still better than grant identifier in my opinion.