As is usual, the first error is the one you need to care about (first). All subsequent errors are likely just caused by the first:

LinkParser.xs:5:27: error: link-includes.h: No such file or directory
[download]

So, you need to find a file named link-includes.h somewhere on your disk. Looking into the README file of the Lingua::LinkParser distribution, it says (somewhat unrsurprisingly) that you need to have the LinkParser extension already compiled and installed. So I guess the next thing to do is to do just that.