Howdy stranger! 
Your Lovense Sex Machine uses a linear actuator to do its thing which is completely different from the vibrators in your Lovense Flexer. I highly recommend checking this handy list and clicking on the “+” sign next to the picture of your toy to look at the specifics of what mechanisms are in your toy and allowing it to do its thing.
Yes, you were correct in guessing that the reason it isn’t working is because the toy isn’t vibration based. Most “normal” games like Dark Souls 3 only output vibrations and the GHR is just simply listening for vibration signals from the game and directing them to your sex toys. There is currently no way for the GHR to translate those signals into the actuating motions needed for your sex machine to work and most games don’t have built-in support for actuating and oscillating toys like your sex machine. In other words, there is unfortunately no way right now you can make Dark Souls 3 work with your sex machine and live out every Dark Souls fan’s fantasy of getting impaled in real life by it as the Nameless King impales your character in-game using his massive, powerful, hard and beautiful spear as his pet dragon jealously watches the action from afar wishing it was him being impaled… I am very sorry. 
With that said, there are some games and mods for games out there that seem to be adding actuator and oscillator support via Intiface that you can check out on this other handy list and also keep an eye on this forum post to see requests submitted for game mods or other software projects that may in the future support actuating and oscillating toys. In any case, even though you can’t be impaled by the Nameless King right now, you are lucky enough to own a pair of pricey Lovense toys which means that your toys are probably very well supported by the Lovense app and the pretty large library of games supported by Lovense themselves, so not all is lost friend! 
EDIT: So apparently qdot might be working on adding support for non-vibrating toys according to this issue on the GHR Github repo. In the future you might be able to be impaled by the Nameless King while playing DS3, but not now unfortunately!