I am an Administrative Official for a large organization. Uploading grants is literally a major part of my job. (As a research scientist, I also write my own grants - so I understand this from several angles.)
The argument that open standards should be used is a fair one, but it is missing the bigger picture here. The vast majority of grants (NIH, NSF, Veterans Affairs, DoD, etc.) are SF-424 NIH standard packages obtained through Grants.gov and submitted by an AO such as myself, not by the applicant. Very few grants require the person authoring them to be the signing official who agrees on behalf of the organization to administer funds if the grant is successful. The vast majority of the applicants therefore route grants through a corporate or University network, where Windows (and to a lesser degree OS X - I'm a Mac user myself) predominate. In all of these cases, the organization will be providing the tools necessary - Acrobat is handed out like candy in my organization. It's part of the corporate image for all computers. Using Acrobat forms streamlines and simplifies submission for 99% of the applicants. The government is not going to change this to address a few edge cases.
The suggested alternative - web forms - is laughable. It might be good for one person, but in an average submission cycle I am sending 10-15 grants with widely varying requirements including esoteric formatting issues, hard-coded naming conventions, and etc. - not to mention that the typical grant includes dozens of required components and attachments, each with set formatting restrictions. It is hard enough to comb through an assembly SF-424 package to check for errors prior to submission as it is. If I had to manually upload each of these grants, one at a time, one piece at a time, into a web forms system, I would not be able to do my job. Period.
Post-submission, forms are processed by a clunky system in eRA Commons, then get referred to Grants.gov for eventual routing to the reviewing agency. The system has a series of automated checks built in to verify that the package is complete before it is assembled. This requires the various bits and pieces to be separate documents, as they are in an Acrobat package (and it is a package, with embedded attachments, not a flat PDF). This process is flaky and fragile enough as it is. Web forms are not going to improve the process, but they certainly would increase the workload for the AO by about 1000% and would definitely increase the error rate. This is also ignoring the fact that the forms are modular, in that some sections (like the budget) are only inserted as needed, and the necessity of being able to assemble and pre-check these things offline precludes any kind of web form system. The article writer is being intentionally obtuse and a bit naive here to make a shallow argument in favor of open standards. Heart is in the right place but reality is being ignored here.
Tl;dr version: it's hard. We do the best we have with the tools provided. Just be glad Grants.gov didn't decide to use InfoPath instead of Acrobat.