However I'd argue with you about Apple. Like you said, Apple didn't hit the time-frame requirement. Wouldn't you also agree that a true startup needs to have the requirements you listed but at the same time start from zero. Companies that just start out, have the growth you talk about in the time frame you talk about would definitely be startups. Companies that have been around for a while and suddenly have explosive growth and hit the other requirements only resemble startups. Google, Apple, and Facebook feel like startups but have certainly grown out of that phase. Being a startup in my opinion a one-time phase that you cannot go through again once you're established no matter how explosive your growth is.
In any case I like your definition and I think it's important that we have one. The word startup is easily overused in an attempt to attain that cool factor some companies have and to ride a trend instead of getting by on the companies real merits.