This is a follow-up question.
@moewe's brilliant solution works. But, when I try to get the Bibliography in trad-alpha style, then the citation keys are not shown in Chapter references (notice the red dots before the items):
The final Bibliography is perfect (notice the yellow highlights): 
How should I modify the MWE to fix this problem?
% https://tex.stackexchange.com/a/372872/38244
\documentclass{book}
\usepackage{filecontents}
\begin{filecontents}{chapterref.dbx}
\DeclareDatamodelFields[type=field,datatype=literal]{
shortdesc,
}
\DeclareDatamodelEntryfields{shortdesc}
\end{filecontents}
\usepackage[backref, refsegment=chapter, datamodel=chapterref,
style=trad-alpha % https://tex.stackexchange.com/a/69706/38244
]{biblatex}
\usepackage[colorlinks]{hyperref}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A. and Duthor, D.},
year = {2001},
title = {Alpha},
shortdesc = {Conference1},
}
@misc{B02,
author = {Buthor, B. and Euther, E. and Futher F.},
year = {2002},
title = {Bravo},
shortdesc = {Journal2},
}
@misc{C03,
author = {Cuthor, C.},
year = {2003},
title = {Charlie},
shortdesc = {Workshop},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\makeatletter
\defbibenvironment{chapterref}
{\list
{\printtext[labelnumberwidth]{%
\printfield{labelprefix}%
\printfield{labelnumber}}}
{\let\blx@anchor\relax
\setlength{\labelwidth}{\labelnumberwidth}%
\setlength{\leftmargin}{\labelwidth}%
\setlength{\labelsep}{\biblabelsep}%
\addtolength{\leftmargin}{\labelsep}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}%
\renewcommand*{\makelabel}[1]{\hss##1}}
{\endlist}
{\item}
\makeatother
\DeclareFieldFormat{shortyear}{\mkbibshortyear#1}
\def\mkbibshortyear#1#2#3#4{#3#4}
\DeclareBibliographyDriver{chapterref}{%
\usebibmacro{begentry}%
\renewcommand*{\finalnamedelim}{\multinamedelim}%
\DeclareNameAlias{author}{labelname}%
\DeclareNameAlias{editor}{labelname}%
\DeclareNameAlias{translator}{labelname}%
\usebibmacro{author/editor+others/translator+others}%
\setunit{\addcolon\space}%
\printfield{shortdesc}%
\setunit{'}%
\printfield[shortyear]{year}%
\usebibmacro{finentry}}
\defbibheading{chapterref}[References]{%
\section*{#1}%
\markboth{#1}{#1}%
}
\defbibheading{bibliography}[Complete Bibliography]{%
\chapter*{#1}%
\addcontentsline{toc}{chapter}{#1}%
\markboth{#1}{#1}%
}
\begin{document}
\chapter{First Chapter}
Some more text \autocite{A01,B02}.
\printbiblist[heading=chapterref, segment=\therefsegment]{chapterref}
\chapter{Second Chapter}
Some text \autocite{A01,C03}.
\printbiblist[heading=chapterref, segment=\therefsegment]{chapterref}
\printbibliography
\end{document}
