It seems that Sierra has a different opinion of what constitutes the current working directory (CWD) compared to previous versions of OS X.
On my computer, Gideros is installed at
/Applications/Gideros Studio/Gideros Studio.app/Contents
(with subdirectories under this including MacOS which contains the actual executable).
Previously OSX would take the above directory to be the CWD so, the path
../../Examples/Graphics/Bird Animation/Bird Animation.gproj
would find the correct file.
But now it looks like the CWD is taken to be somewhere else. If so this is going to break hundreds of programs not just Gideros and it's a simple Apple bug which they will no doubt fix. (I can't believe this is a 'feature'!)
I also found this website which lists numerous bugs in Sierra:
I think this section might be relevant:
“The application ‘name’ can’t be opened” or Error -41
Unfortunately the solution is to reinstall Sierra!
Note that this problem only occurs in Sierra not in previous versions of OSX. However, @hgy29 has installed Sierra without encountering the problem. I have not upgraded from El Capitan yet as I am afraid such a buggy release of OSX will break the build system. I'd rather wait till things stabilise before upgrading.