Earlier quoted context omitted.
I mostly agree; the only caveat I'd give is that it's tough to say how much longer any of us are going to be yuppies right now; I work for one of the many big megacorporations whose stock is tanking right now. If the stock doesn't pick up soonish, there's a non-zero probability of me being laid off. While I'm not that worried (I've been able to find work in bad economies in the past), I also do feel a bit of paranoia…
Why? The price of the stocks does not affect company in any way. If the company sales are going down or clients stop coming this is an issue, stock value is important only for those who hold/speculate using them. You company has already got the money from selling stocks, nobody is going to take them away.
That would be the case in the ideal world. However, stockholders care a lot about stock prices being low, and they elect the board, which in turn chooses/advises the CEO (and other executives). When it's the CEO's butt on the line, the company will be reactive to share prices; just to make sure the stockholders are happy.
A secondary concern is that low share prices makes a company vulnerable to non-/hostile takeover bids - which again is bad for CEO job security.
TL;DR: The tenure of the top echelon (board & executives) of public companies is directly tied to (relative) stock performance due to share voting rights.