try this:

key=key.replace(/ /g,"_");

that'll do a global find/replace

javascript replace

As of others have explained how to do it using str_replace, you can also use regex to achieve this.

$name = preg_replace('/\s+/', '_', $name);

You can use expl3 that's more robust than xstring (and more flexible).

\documentclass{article}

\ExplSyntaxOn

\NewDocumentCommand{\filter}{m}
 {
  \tabraham_filter:n { #1 }
 }

\tl_new:N \l__tabraham_filter_text_tl

\cs_new_protected:Nn \tabraham_filter:n
 {
  % set the tl variable to the lowercased version of the input
  \tl_set:Nx \l__tabraham_filter_text_tl { \text_lowercase:n { #1 } }
  % replace spaces with underscores
  \tl_replace_all:Nnn \l__tabraham_filter_text_tl { ~ } { \_ }
  % deliver the result
  \tl_use:N \l__tabraham_filter_text_tl
 }

\ExplSyntaxOff

\newcommand{\questionsection}{Game of  rolling   dice}

\begin{document}

\filter{\questionsection}

\filter{Game of  rolling   dice}

\end{document}

You may want to define a filtered version of some token list, so when using it you don't have to repeat the whole process.

\documentclass{article}

\ExplSyntaxOn

\NewDocumentCommand{\filter}{m}
 {
  \tabraham_filter:nn { #1 } { \tl_use:N }
 }
\NewDocumentCommand{\newfilteredcommand}{mm}
 {
  \tl_if_exist:NF #1
   {
    You~don't~want~to~silently~redefine~something,~do~you?
   }
   {
    \tl_new:N #1
    \tabraham_filter:nn { #2 } { \tl_set_eq:NN #1 }
   }
 }

\tl_new:N \l__tabraham_filter_text_tl

\cs_new_protected:Nn \tabraham_filter:nn
 {
  \tl_set:Nx \l__tabraham_filter_text_tl { \text_lowercase:n { #1 } }
  \tl_replace_all:Nnn \l__tabraham_filter_text_tl { ~ } { \_ }
  #2 \l__tabraham_filter_text_tl
 }

\ExplSyntaxOff

\newcommand{\questionsection}{Game of  rolling   dice}
\newfilteredcommand{\questionsectionfiltered}{\questionsection}

\begin{document}

\filter{\questionsection}

\filter{Game of  rolling   dice}

\questionsectionfiltered

\texttt{\meaning\questionsectionfiltered}

\end{document}

The last line is to show that \questionsectionfiltered is what's expected.