  Let $(M,F)$ be a connected Finsler space. An isometry of $(M,F)$ is called a
Clifford-Wolf translation (or simply CW-translation) if it moves all points the
same distance. The compact Finsler space $(M,F)$ is called restrictively
Clifford-Wolf homogeneous (restrictively CW-homogeneous) if for any two
sufficiently close points $x_1,x_2\in M$, there exists a CW-translation
$\sigma$ such that $\sigma(x_1)=x_2$. In this paper, we define the good
normalized datum for a homogeneous non-Riemannian $(\alpha,\beta)$-space, and
use it to study the restrictive CW-homogeneity of left invariant
$(\alpha,\beta)$-metrics on a compact connected semisimple Lie group. We prove
that a left invariant restrictively CW-homogeneous $(\alpha,\beta)$-metric on a
compact semisimple Lie group must be of the Randers type. This gives a complete
classification of left invariant $(\alpha,\beta)$-metrics on compact
semi-simple Lie groups which are restrictively Clifford-Wolf homogeneous.
