Vertical alignment of a row after use \shortstack

What about using makecell?

\documentclass[12pt,a4paper]{article}
\usepackage{blindtext}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tabularx}
\usepackage{blindtext}
\usepackage{booktabs}
\usepackage{makecell}
\begin{document}
    \begin{table}[htb]
        \footnotesize
        \begin{tabularx}{\linewidth}{cX}
            \toprule
            \textbf{\makecell{Line 1\\Line 2}} & \textbf{Head}\\
            \midrule
            Parameter 1 & \blindtext \\
            Parameter 2 & \blindtext \\
            \bottomrule
        \end{tabularx}
    \end{table}
\end{document}

Use a \Centerstack from the stackengine package. Not only does it achieve the desired centering, it gets the line spacing correct (by fixing the baselineskip, rather than the inter-word vertical gap in the manner of \shortstack).

\documentclass[12pt,a4paper]{article}
\usepackage{blindtext}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tabularx}
\usepackage{blindtext}
\usepackage{booktabs}
\usepackage[usestackEOL]{stackengine}
\begin{document}
\begin{table}[htb]
\footnotesize
\begin{tabularx}{\linewidth}{cX}
\toprule
\textbf{\Centerstack{Line 1\\Line 2}} & \textbf{Head}\\
\midrule
Parameter 1 & \blindtext \\
Parameter 2 & \blindtext \\
\bottomrule
\end{tabularx}
\end{table}
\end{document}