It will take a while. Desktop software will be irrelevant shortly, as will the personal computer as we knew it. Companies will redeploy internal desktop apps as web apps, first to their own servers, then for cloud platforms like GAE.
Microsoft is doomed. This is its future.
Shortly? To me, it's pretty damned irrelevant now.
Desktop software will never become irrelevant.
I will continue to choose MS Word for the foreseeable future because the documents are on my machine, and not on the web where it is vulnerable to MITM attacks or the whim of Google employees and government agencies.
And, BTW, by being on your machine, they may not be vulnerable to government agencies (unless you cross a border) and Google employees, but, as was shown a couple weeks back, it's vulnerable to borked anti-virus updates.
Not to say the viruses themselves.
I guess it depends how you define dying, dying as in no longer being the most influential player in all of computing, probably. Dying as in a failing business with in eventually go bankrupt or sell, not a chance from where I'm sitting.
There is no mercy for those who make things the market doesn't want.