Glad you solved it. I was gonna suggest that you needed to install make through cygwin, and/or set your default shell to the cygwin one.
But it seems that a regular install of make worked 
The output of those commands looks scary, but it does have a kind of sense to it: it’s a colon-seperated (with these: : ) list of directories. The directories generally at the root of your C drive, which is /c/ in cygwin. When you run a command, every directory in that list is checked to see if it has a program file with the name of that command.