You may follow Gentoo Wiki (or other guides) to install steam in chroot first. But you may failed to launch games like Dota2, because steam is using something called soldier and bwrap.
The steam.sh below can make soldier and bwrap work by mount chroot_dir twice. this works fine for me.
Save steam.sh file to /usr/local/bin/steam, so you can run steam command in terminal to launch steam, or add steam deeplink like steam steam://install/xxx.
To start steam without ask sudo password, add this to your sudoers file:
%wheel ALL=(ALL) NOPASSWD: /usr/local/bin/steam