You need to have another look at the picture. The output of the encryption process actually denotes $R_{n+1}$ on the left side and $L_{n+1}$ on the right side. And the input to the decryption function has the exact same order, so you don't have to swap anything manually, they are just 'labeled wrong'.
The reason here is that the last round is actually not exactly like the ones before, because it does not contain swapping the two halves. A more obvious way to express this would have been to do one final step like $L_{out} = R_{n+1}$, etc. and then start on the decryption with Left/Right labeling.
Also, I don't understand what they want to indicate by the green and red arrows. The coloring in both sides is either inconsistent or simply wrong. It also indicates that $n$ is an even number.