The explanation page that you linked to is very helpful and clear. You’ve got the idea but you’ve reversed the letters on both the white side and the black side so that they read right to left. Go back to the explanation page and graph the letters step by step as shown in the example.
For the first photo, the white side, the I and N should be to the right of the W (WIN). For the second photo, the black side, the I and the N should be to the left of the G (ING). When you flip the hat back and forth you should be able to read the letters left to right on each side.
When you’re knitting the hat, the W should be knit at the same time as a backwards G, the I should be knit at about the same time as the backwards N. [The letters won’t be knit one for one because some will take up more width (e.g. W) than others (e.g. I).]
I see some complaints on the Ravelry page about the hat being too big so going down a couple of needle size is probably a good idea. You can use the project thus far to give you an idea of how much too big it may be. It’s going to be a fabulous looking hat. It’s just a matter of getting the first couple of rows set.