Yes. It would mean that even if it was not an all cash deal. Yahoo! bought 100% of Tumblr and owns them outright.
They would even if it wasn't an all cash deal.
Well, if tumblr employees got Yahoo stock, they could use it to influence the direction of the company, at least a little.
A more extreme example of this would be that when Disney bought Pixar, Steve Jobs became Disney's largest individual shareholder (7%) and joined the board.
Or when Apple bought NeXT, and shortly there after Steve became the CEO again. Apple did the buying, but NeXT was still in control.
Cash or not, won't the buyer have absolute power over the property (Tumblr)?
Yes but if you buy them with stock they get some of that power (since the power in the end belongs to all the shareholders)