How does Red Windsor cheese get its colour?

From the port wine! Yum!

Red Windsor is a pale cream English cheddar cheese from Leicestershire, made using pasteurized cow's milk marbled with a wine, often a Bordeaux wine or a blend of port wine and brandy.

https://en.wikipedia.org/wiki/Red_Windsor_(cheese)

Depending on the maker, the effect can look more pink than red. The technique is similar to making a marble cake - mixing the plain cheese and the coloured cheese to create the patterning. It's not always suitable for vegetarians as artificial colourings are sometimes used. The proportions of pink and red vary according to the maker - some versions are almost completely coloured red. https://www.gourmetdash.com/cheese/windsor-red-cheese-10341-config