I have not looked into this issue of Lumonisity extensively, but did so a bit.
They make a lot of claims and don’t cite to the primary psychological literature, which is always a warning sign.
OTOH, there is a fairly well described set of improvements which occur in specific subdomains, like working memory, with some training tasks.
I thus suspect some of Luminosity’s games will help improve scores on some sub-tasks in the Cogscreen aero, though am not aware of any specific studies of their games in this regard. The anecdotal evidence on PoA supports this.