Version 10.1 is only supported by Photoshop Elements 2018 and later so you'll never be able to open Raw files from that camera using Elements 15. Elements 15 only goes up to Camera Raw 9.10 (nine point ten).
You can, however, download the free Adobe DNG converter and convert all your A7R III Raw files to DNG format. You can then open the converted DNG files (not the Raw files) in Elements 15. An extra step for you but no extra cost.