I tried to update script, and after that, new version of the script even told me, that 4.3 is not supported. There in no "install from binary" at all for me. I can install from source, but it gets some old version too (some 1.6.9), and it is not working properly (glitches and freezes).

This means you're running an RetroPie version based on Raspbian Jessie, which is no longer support by Raspbian and - alas - by RetroPie also.

You should try and upgrade by imaging with the latest version of RetroPie (4.5.1) and you can backup and restore your settings and roms using the method mentioned int the Docs.