A VPN isn't always an extra hop from a "hops in traceroute" perspective. It's very possible to get a shitty route from your ISP; e.g. if the best route goes through an ISP that your ISP has shitty peering with. You might get better latency via a VPN to a server inside the "best route ISP" network, because then your ISP _has_ to route your traffic through that peering exchange. I.e. the additional latency of doing the VPN stuff is still less than the additional latency of having a poor route.

Hops also aren't a particularly useful abstraction here. They don't align with latency very well; the only thing a hop implies is that a router has to get the packet and route it, but that's a huge variance in latency. A hop could take nanoseconds or it could take hundreds of milliseconds. The number of hops doesn't really imply anything useful about latency.

All that is to say that yes, I believe under some circumstances the VPN could give you lower latency (with a bunch of asterisks). One asterisk is that figuring out whether your peering is good or bad practically requires a network engineer to look at your routes, it's not an easy thing to figure out. A second is that those routes change frequently, so just because the VPN helps today does not mean that it will tomorrow or even for the next hour. A third is that these solutions are likely somewhat custom; each ISP or maybe even each network segment will have particular links that need to be avoided, which means each ISP/network segment will have particular IP ranges that "encourage" the correct routing. Figuring out which to use would be non-trivial.

In TLDR form, I think a network engineer willing to spend like 4 hours analyzing their network to set up a VPN that will shave 5-10ms off their latency to a particular game for a limited amount of time could probably do so. It's within the realm of possibility that some company is doing a Thousand Eyes-like thing and actually creating optimized VPNs with the same strategy. My suspicion, however, is that they just tell you to log in and try your latency on a bunch of servers til you find one that's lower (at the present moment) and then they hope you never check again.