Actually the rules permit it,
Rule 8
Section 8. RUNNER IS NOT OUT
B. When a runner does not run in a direct line to a base, provided the fielder in the direct line does not have the ball in their possession.
The runner didn't touch first base, if they did, for some unknown reason, then they would need to retouch second. There is no reason they need to retouch second.
That rule has absolutely nothing to do with the play posted, it is simply saying a runner is not out if they do not run in a direct line between the 2 bases.