Is it possible to install mysql 5.7 on Amazon Linux AMI?

If you are using mysql/Oracle repos you should select Linux-generic in the Download MySQL Community Server page for AMI boxes and not RedHat/Fedora packages.

Last time I checked AMI does not run systemd hence the error. While in past you could somewhat get away with installing RH packages in AMI Linux, nowadays with the convergence of Linux versions to systemd it is ever more difficult to install foreign packages in distributions which do not support systemd.

File also a bug/request with Oracle for AMI rpm packages, please.

Check also what versions can you find in AMI repositories, just in case.