res_yy.sty is based on res and issues
\nofiles % resume's don't need .aux files
See also *.aux file not generated
Apparently, the assumption resume's don't need .aux files is wrong, since you want a bibliography and bibliographies often rely on auxiliary files.
You should look into different, more modern document classes for a resume. \documentstyle is old LaTeX 2.09 syntax that has been outdated for more than twenty years now. http://www.yisongyue.com/resume/ even mentions
NOTE - This template is provided "as is" and is no longer actively maintained. Systems using newer versions of LaTeX might have some compatibility issues with this template.
So you really should not expect this class to work properly any more with a modern package like biblatex (biblatex is a good 15 years younger than LaTeX2e, the successor of LaTeX 2.09). In fact if you run your MWE on a modern TeX distribution you get quite prominent warnings
Entering LaTeX 2.09 COMPATIBILITY MODE
*************************************************************
!!WARNING!! !!WARNING!! !!WARNING!! !!WARNING!!
This mode attempts to provide an emulation of the LaTeX 2.09
author environment so that OLD documents can be successfully
processed. It should NOT be used for NEW documents!
New documents should use Standard LaTeX conventions and start
with the \documentclass command.
Compatibility mode is UNLIKELY TO WORK with LaTeX 2.09 style
files that change any internal macros, especially not with
those that change the FONT SELECTION or OUTPUT ROUTINES.
Therefore such style files MUST BE UPDATED to use
Current Standard LaTeX: LaTeX2e.
If you suspect that you may be using such a style file, which
is probably very, very old by now, then you should attempt to
get it updated by sending a copy of this error message to the
author of that file.
If you must use res_yy you will have to modify a local, renamed copy of res_yy.sty yourself since \let\nofiles\relax before \documentstyle does not work.
Rename a copy of res_yy.sty to res_yy_ab.sty, find the \nofiles statement and comment the entire line by placing a % before it.
Then modify your file to load \documentstyle{res_yy_ab}.
But really the answer is to not use this document style.
\]documentstyle? that's latex 2.09 syntax. it's been out of date since 1995.\documentclassis the current equivalent. i wouldn't expect any of this to work properly with\documentstyle. – barbara beeton Dec 12 '17 at 01:57yy_res.clsis based onres.clsand also uses\nofiles, butbiblatexneeds auxiliary files. – moewe Dec 12 '17 at 07:30\let\nofiles\relaxbefore\documentstyle{res_yy}as suggested in the linked answer? Of course the real answer is not to useres_yy. – moewe Dec 12 '17 at 09:27