I can’t comment on Google specifically but it is possible to have de jure controlling interest, while another party has de facto control because they can threaten to unload a huge position and tank the price.
These people are not forced to make more money at the expense of others. It's their choice.
If the threat is that unloading a position will cause a dip in shareholder value of $X, but those actually in control believe their own thesis and operating model is worth more than $X, then they can choose to weather the storm, believing their way will negate the loss of $X.
If they really don't have an answer to the activist investor's thesis, then yea, they'll roll over.
Don't be that kid.
More likely, though I haven't read their letter in depth, is that their beliefs actually aren't that far out there - I mean, you probably aren't going to get pushback from anyone if you say "Google is bloated and needs to trim and focus". So they write a letter and make some noise, and then when Google makes some rather unsurprising changes they can say something like "look how influential and prescient we are", and that has value in the investment world.