In the first step of the reaction the chiral center in the starting material is lost. So the chirality of the starting material, even if it is enantiomerically pure, won't be transferred to the product.
I would just like to point out that there is a chiral centre at S in the sulfoxide and (probably more importantly) the allene has axial chirality. So I'd say it's actually inevitable that stereochemical information is transferred to the product and expect it to be stereospecific.
A further comment: The starting alcohol is
S-configured in the question, but the original poster has drawn a mechanism starting from the
R-configured alcohol - it would appear that the centre was accidentally inverted on redrawing the starting material in a different conformation to that provided in the question.
If you work through the mechanism showing the stereochemistry of the allene, it is not too difficult to rationalise the configuration at the quaternary C centre and choose conditions for B
final product (thermal or photochemical). You can also predict the stereochemistry at S in the product, which is not given in the answer (I'd go for the
R-configured sulfoxide, but I will wait for the OP to have a go at it before showing my arguments).