Fischer Tropsch synthesis is old technology. It is merely that Shell has a massive (>$20B) investment in these types of plants. There is something to be said about leveraging GTL to lubricants versus crude/wax/gas to fuel liquids, given the distribution of products and the post-processing necessary, which is hydrogen intensive.
FT does indeed produce LOTS of waxes, so dont think for one minute that the Grp III GTLs arent derived from a wax source similar to how standard Grp IIIs are derived from slack wax.
But there is a benefit in that there is a bit more intrinsic control of the processes, rather than dealing with wax byproducts that could change daily in their sourcing.