He lost a year of Cespedes for a shot to go for it. Cespedes would have been gone after next year, because we know the A's are not going to pay anybody. He gambled and took a shot figuring his pitching wasn't good enough. They were ousted the last 2 years by stud pitching, despite having home field advantage. You need front line pitching to get a chip and the last 2 years provided the proof.
You said it yourself, championship or bust. The way they did it before did not work. You need front line pitching. Unfortunately, acquiring top line starters comes at a cost. You can either spend big money, trade great players, or trade top prospects. The A's (as evidenced by their payroll) do not spend money. So, you have to trade great players or future great players.
Lester didn't pitch great tonight, but he had been pitching well (both he and Samardzija) and he is a proven playoff performer. He also left the game with the lead.
Beane was also smart enough to acquire a defensive catcher that would have helped shut the Royals running game down. Unfortunately, he got injured in the 1st inning. Tough break that probably changed the outcome of the game.
Maybe the trade hurt them, maybe not. But they are never even close to the position where he could hurt them without amazing GM work.