So, if you've been on my profile recently, or have checked out this topic of the forum, then my idea of falculatively bipedal dimorphodonts is nothing new to you. But I never actually explained it in depth. I had plan to start this blog post series anyway, so here's my explanation of (semi-)bipedal pterosaurs.
Also, this, and most further concepts done in this blog post series are about concepts, not application, so I won't talk about any scenario's to do with this, simply how the evolution and bauplan could work.
Firstly, I'll describe the basic concept. In an alternate Jurassic, dimorphodonts start running on their hind legs when sprinting. Otherwise, they walk on all fours, but running frees the hands to grab prey. This allows them to grow into large predators on the fern prairies. Now, this leaves the problem of why they evolved to chase prey this way.
The solution lies in forms that wouldn't be as derivative from other dimorphodonts. Instead of running, the use of the fore-limbs for grabbing would instead come from jumping. In this case, at prey. Jumping up in a large arc then coming down on some small lizard or such. This would probably come about to get on top of prey about it's size, or a bit smaller.
Eventually, they might be jumping from a distance. This would lead to them pushing off their legs again after the jump, extending to reach the prey. Extend this more, and over time, they start running on their hind legs to catch prey. At one point or another they're eventually sprinting.
This would mean back legs adapted to running. They forelimbs would be shorter, although erect, as the creature wouldn't need it's back parallel to the ground. It'd probably benefit from a low skull, actually.
This frees up the forelimbs. Claws would develop, and they become more muscular to hold and restrain prey. The teeth would converge with those of theropod dinosaurs, and become serrated. These features would allow them to hunt large prey. Eventually larger forms could evolve from this.
They'd be able to continue running based on the constant speed alone. The legs wouldn't be able to support them upright at a slower pace or standing still, given the large skull of dimorphodonts (which could be further enlarged here, thought smaller compared to the body size). A long, stiff tail would help.
Would they become flightless? It would depend on how developed the forelimbs become for hunting. I'm also not sure about stopping. Perhaps remnants of wings could help here, jumping up and flapping to control the fall. Full flight would be unlikely to stay, however.
And why dimorphodonts? They were a mostly inland terrestrial group, and already used large skulls to hunt small prey. They would be the only logical candidates for this to happen.
How would these fair against competition? Assuming a no/alternate T-Jr, or evolution in general early in the Jurassic, theropods would be re-written. They have to evolve and ambush prey in forest at first, then at the edges of forests, where there is open space to chase prey. It would depend on if large theropods or pseudosuchians were already in niches that would heavily compete. Given the chance to evolve, these could be successful in the short term. Long term, they'd fall to the changes nature throws at it. They simply wouldn't adapt well at this point.