We're back to trying to operationalize "grief," it looks like.
I think that people can grieve for things they never had but always planned for, particularly if the desired outcome is strongly attached to self-concept/identity, as CWard12213 mentions. One example would be a client who worked hard to get through college, but failed math 4 times even after seeking tutoring, etc. and changing his tactics each time to try to pass. He was stuck without a degree and in a dead-end job, grieving for the loss of careers that were no longer options to him. This was not a small setback to him, but life-changing, and caused a lot of distress because he didn't know what to do with his life now that his chosen path was not available. His emotional experience closely resembled Kubler-Ross' stages of anger, denial, depression, etc., and my past supervisors encouraged me to frame it as grief/loss of career. Or what about folks who take the EPPP 4 or 5 times and eventually just give up on ever getting licensed and have to change their career plans? That would involve grief/loss for something you never had, but spent years working toward (a license).
Having said that, whether or not the OP and grad school applicants can experience grief or loss after one unsuccessful application round is debatable and subjective, and of course, we shouldn't minimize or pathologize either way.
I think what people in here seem to be speaking to is the grief-heavy language on the OP's support website that attends strongly to grief and loss aspects of unsuccessful applications...it comes off a bit strong, although I understand the intent. Language matters, and in this case, it's important not to go too far with ideas or overstate things. I can't speak to whether the grief and loss is "valid," but I'd be cautious about how I express ideas (and share personal information) on a public website.