Hey, here's some lore concerning the really odd crossbow which, to my eye, wouldn't work well compared to our version of crossbows. But oh lore, you wonderful reset button!
Do take this with a grain of salt; the lore was purposefully left vague and open to interpretation.
The "Vaulter's" faction is an ancient one, tied with a long-lost people called the Endless . To explain the Vaulters, I have to explain what the Endless were doing: They were a space-faring empire, unequal in their power or wisdom, but weak between themselves. Their scientific brethren (the "Virtuals", those who uploaded themselves into computers forever-repaired by Dust nanobots) embraced the concept of becoming virtual gods, while their physical-bodied brothers (the "Concretes", who would live organic existences with Dust maintaining all of their needs) rejected the notion. Soon after, civil war consumed them both, and naturally everything they built (mostly with Dust) was left behind for others.
One of these relics was a massive xenoresearch station, tasked with creating artificial habitats to study all the little critters found in the galaxy, aptly named the "Husk of Knowledge". The Endless, being nigh-omnipotent, only limited the size of their creation to what they considered "appropriate", which turns out to be the size of half a continent and as tall as a mountain. (Do consider, they were gods at this point)
Finally, we enter the beginning of the Vaulters. The original descendants were survivors of a destroyed spaceship orbiting the planet, lucky enough to escape in a pod not sold by the wrong salesman. They crashed into the aforementioned Husk of Knowledge, and managed to survive within the massive confines of the structure. The survivors established themselves within a safe haven inside the Husk, using their limited findings and technologies to fend off the hostile bugs and whatnot still living inside the station.
There's not much explanation at this stage, but we can still imagine what happened. The survivors would eventually begin running out of their precious technology (ammo, armor, energy, production, stuff a convict wouldn't know off the top of his/her/it's/schlarg's head). Improvisation and retrofitting would be standard at this point: no bullets? What a shame, but hey that string and those sticks could make this rifle mechanism into a crossbow if I repurpose it enough. Power armor ran out of power? Sure, take out the battery and electronics, and only leave the metal bits. Eventually, you'd be left with salvaged weaponry that you know how to make, using organic and locally-sourced resources (most aren't healthy though).
Finally, we get to the Vaulters. The survivors would settle and create a small town, which would naturally grow. That ramshackle technology made to work with whatever scraps they could find was suddenly the best that they had. The knowledge would be infinitely valuable as well; why create a new crossbow when you can replicate the riflebow your predecessors crafted before? Why not upgrade it further? Why use wood when there's barely any inside this alien building, but there's plenty of metal literally everywhere you look upon? I'd imagine this process would continue until the actual emergence of the Vaulters as a surface faction: the knowledge of their ancestor's weapons and re-purposed equipment would be kept in the refined and improved designs of later generations, but the knowledge of the ancestors themselves would be lost because of the length of time between "colonization" and emergence, and a severe scarcity of pencils (sometimes limbs). Try writing down the blueprints for an M-16 while stuck inside the Himalayas with aliens all over you. Yeah...
Still, the riflebow itself would suit their needs fine from a geographic perspective. Considering you're an underground race that fights in dark, cramped tunnels full of godless aliens, horizontal shoulder room would be at a premium but vertical space would be plentiful: enter the vertical crossbow limbs and heavy armor+shield combo. The shield and armor would stop the attack, vertical c-bow limbs would allow for horizontal maneuvering, and the range of the crossbows means you can deal with enemies at range. Pretty nifty for a one-in-all package.
So yeah, that's it. TL;DR the "riflebow" evolved from the need of the original survivors to make their useless weapons useful once again, and the design stuck with the original Vaulters because it worked for them in their environment, as well as being convenient to use previous knowledge and build upon it than trying to reinvent it all over again. I'm sure they found a way to use it effectively (muzzle-loaded bolts, side cranks, grooves on their shields) given their thousands of years using the thing and refining it. Also some things are just convenient, like straps taken from an absolutely ancient rifle that the marines found really convenient. (kid you not that's what the units are called).
Also that's why I love this franchise; the interconnected lore and boatloads of backstory allow entire pages of lore to be filled.
For a CROSSBOW.