Links tunic is made that way obviously mainly for fashion.
We can break it down into 3 pieces (2 matching). The front/back and then the 2 sleeves.
This type of front/back without the sleeves is a common surcoat.
The sleeves on the other hand are likely 100% style choice, but it could also be that the tunic is a much more solid construction and needed to be slit and the designer simply liked this better than stitching it, or that are designed to connect to some other armor piece to support it, but what this could be, who knows. There is however, no shirt design that has such lacing I know of for the sleeves.
It could also just be there to reinforce the stitching which is often enough done on older clothes so that you have two levels of stitching/lacing that takes off tension and makes it less likely to tear. This is definitely somewhat true of the cap.
So there is functionality to why they are be there, but there are also design choices.
Also Link's Tunic is Actually a Surcoat (a weird one at that), over Leather armor, over a cotton or Linen Gambeson