Why do you want to use SAML? You should use OpenID Connect for all new application integrations.
And yes, that document is for the AWS console, which is a hosted service. You are talking about a website that is hosted on AWS. They are completely different requirements.
As I said, you just need to implement SSO to your app.
If you really want to use SAML, install the Shibboleth SP software on your application's web server. [read the docs](https://gluu.org/docs/ce/integration/webapps/saml-sp/).