Figured it out. If anyone runs into the same problem, here is the fix which helped me.
First I tried to install FreeType again using brew.
brew install freetype
The output was:
Warning: freetype 2.13.2 is already installed, it's just not linked.
To link this version, run:
brew link freetype
So I tried to link again. There were already some files under "/usr/local/include/..", so I removed them. "Brew link freetype" now ran without problems.
After that brew install was able to install the game porting toolkit. Yay!