So what if she decided to leave Google and be hired by Yahoo?
Why would she, what does Yahoo have that would make her voluntary leave Google?
How about a CEO title, which looks very good on a resume. IF she can't "save Yahoo" and it does crash and burn, she now has experience running a company at very little professional risk to herself. Yahoo's troubles are well known in the industry, if she staves it off even for a short period then she wins. This makes it easier to transition to CEO of another company in the future, if she desires (but not to public office as demonstrated by Meg Whitman).
Monetary gain? Yahoo can not afford it.
You really are a short-sighted fool, aren't you? When you get to the levels that we are talking here, the "monetary gain" is of little to no consequence. At these levels it is all about title and influence. CEO is the brass ring.
Workplace culture? She was literally the public star of Google. Unless things have changed radically, Google's workplace is very progressive to say the least.
Same as the monetary response. At these levels, the employees do pretty much what they want. Workplace culture is a buzzword for the lower levels and addresses how happy the average worker is
The deal between Yahoo and Microsoft has what to do with Google? I read the article but didn't see a single connection.
Revenue, lots and lots of revenue. The Deal between Microsoft and Yahoo was an attempt to create a bulwark of adverts, search revenue and online sales revenue against Google by consolidating competition. All of such was bolded in the linked article.
Most of the rest is addressed in the rewritten posts.
This is the only intelligent, non conspiracy driven thing you have posted here. And it doesn't even relate to your point....