As stated by the others, it is a reference to the "rat race" of corporate work. He tried and failed, and thus the "rats won"

I think there's a few explanations, but this is probably it. "rats win the race" refers to "rat race" which is a term used to describe an endless, self-defeating or pointless pursuit. It conjures up the image of the futile efforts of a lab rat trying to escape while running around a maze or in a wheel. This is often used to describe work, particularly excessive work; in general terms, if one works too much, one is in the rat race. This terminology contains implications that many people see work as a seemingly endless pursuit with little reward or purpose. therefore this is saying what ever he does, in the end it will not change a thing(things go wrong) the other possible explanation is the quote “The trouble with being in the rat race is that even if you win, you're still a rat.” ― Lily Tomlin basically, even if you try and win or come out top, you are still who you are and cannot change who you really are otherwise the other possibility is the Chinese zodiac explanation where the rat is the cheatingly lying one that reached first-> you have to lie and cheat your way to victory. if you want to be responsible and stop making excuses then the rat will beat you and you will fail the last one is probably not it though...

I think it is refer to the term "Rat race". It basically means that they go through a lot of effort to achieve a pointless or self-defeating pursuit. Think of it of a rat on a mouse wheel, it goes though so much effort to achieve nothing. Even if you win, your still achieve nothing.