The gap can make a huge difference, specially if you don't pay attention to how the water flows/sprays in the shower.

We didn't have the best shower/glass people in our build and our gaps are similar.

There are sweeps/seals you can add to the glass to keep the spray contained, but you might have to try several before finding one that will fit properly. The standard sweeps/seals didn't work on my doors, specially if you want to swing the doors in both directions. I ended up trying Alien Seal flexible tape and it has worked really well. I installed it about 2 years ago on my shower doors and it is holding up great and does the job of containing the water spray.

The gap itself doesn't look particularly unusual--I just tested mine and it's about the same as far as fingers go. Given your hinge style, I doubt you could have too much less of a gap there since they can only adjust so much. What is different about your door is that there's no gasket on the glass to close up the gap. Mine has a rubber piece that runs the length of that side so that it seals, and I haven't used a glass shower door that didn't have some sort of seal or sweep along the edges. Are you 100% sure they are done with the project? (I see some blue tape there so wondering if perhaps the contractors might still be working on some things?) The seals were the very last thing that were put on our doors once the installation was complete.

Most times you would normally shoot for about 1/4", hinge brand and type dependent and I cannot tell enough about that hinge from the picture alone. Not a hill to die on in my opinion and acceptable in my perspective. If it bothers you you can ask the installer but there is zero chance he will replace that, nr should he in my opinion. Get a vinyl hinge seal if you get much water escaping.

I cant see what the other side looks like but typically you would want the hinges on the side opposite to the shower head. That way the panel that will be fixed can have the gaps filled with silicone to crate a waterproof seal. The side with the hinges should be far enough away from the shower head where water wont flow through it.

I assume at this point you probably don't want to pull it out and re do it. You can also buy vinyl channel seal that they make for shower glass doors and try to make do with that. You may need to find the right size and make some cuts to get it right but it's an alternative to ripping it out.

Good Luck!