How can I adjust this code for a vertical enumerate in documentclass{book}?

This answer is based on https://tex.stackexchange.com/a/50452/90297 .

The difference from your MWE:

1. Used the book document class as requested.
2. Put the circled in a newcommand as in the old answer.

Differences from previous answer:

1. Notice that unlike the original, here you can take two parameters into your button, enabling you to use different colors in different levels/lists.
2. Used contour and shading as in MWE.

MWE:

documentclass{book}

usepackage{tikz}
usetikzlibrary{shadows}
usepackage[outline]{contour}

newcommand*circled[2]{
            tikz[
                baseline=(char.base)
            ]{%
            node[shape=circle,
                  minimum size=0.75cm,
                  top color=#1!30!white,
                  bottom color=#1, 
                  draw=#1!90!black,
                  append after command={
                    node[circle,draw=#1!90!white,
                    minimum size=0.68cm,
                    font=sffamily]at(tikzlastnode.center)
                    {textcolor{white}{contour{#1}{#2}}}
                  },
                  thick,
                  general shadow={
                    shadow xshift=.2ex, shadow yshift=-.2ex,
                    opacity=.5, fill=black!50,
                  }
                  ] (char) {#2};}}

usepackage{enumitem}
usepackage{xcolor}

begin{document}

begin{enumerate}[label=protectcircled{red}{arabic*}]
item Step one%
item Step two%
item Step three%
end{enumerate}


end{document}