Should be able to plug your phone into your Mac, and with android file transfer, copy pictures from the photo folder to your computer.
This might sound like I'm just being a d*ck, but I'm actually curious, is there a reason you didn't have them auto backing up?
Unfortunately I'd be a little surprised if you can just plug it into a computer and get photo's off while the phone is locked. I'd be a bit worried if it was that easy for someone to get my photos anyway. As has been said, if they're important, you might just need to get it fixed.
Can't see what I'm controlling the screen is broken.Try plugging in a usb mouse and using that to control the phone
I was doing a bit of brainstorming, and had an idea.
Does the phone support display out via the micro usb?
You could use it to navigate the display
If you had USB debugging enabled try using Android ADB, command line but slightly more powerful than USB file transfer alone.
https://www.howtogeek.com/125769/how-to-install-and-use-abd-the-android-debug-bridge-utility/
Is the screen not showing anything or is it just input which is broken? If you can see something on the screen get a USB OTG cable and plug in a keyboard and mouse?
Are they stored on an SD card which can be removed?
This might sound like I'm just being a d*ck, but I'm actually curious, is there a reason you didn't have them auto backing up?
Unfortunately I'd be a little surprised if you can just plug it into a computer and get photo's off while the phone is locked. I'd be a bit worried if it was that easy for someone to get my photos anyway. As has been said, if they're important, you might just need to get it fixed.
I've got the same issue with a Moto X play - screen completely dead but need to recover some photos.
Can't use usb as you need to see the screen to put it into mtp mode or whatever to transfer files.
From using Moto phones this is the case. Need to confirm on the phone every time you plug it in.
If you send it back to Motorola then ask them not to wipe the phone. I sent one for screen replacement back in the day and they wiped it and installed the already installed latest software version just for laughs I'd try a high street repairer over motorola or even maybe the tech guys at Carphone warehouse who were surprisingly good recently when I used them - though this was a warranty repair.
I'm not tried pushing anything from the play store recently, but can you install something like Airdroid from the play store?
It might install and be set up to run automatically? then you can control the phone from your pc