SSIS Installation on Dedicated Server We are planning on installing SSIS 2016 on a new dedicated ETL server.

The packages will be called from SQL Server Agent (on a separate server), or from an application (again on a separate server).

From reading the Microsoft docs, it seems that we need to install Database Engine along with Integration Services on the dedicated SSIS server. Is Database Engine required on the SSIS server for our needs?

I'm confused by this: "If the ETL server does not have an instance of the Database Engine, you have to schedule or run packages from a server that does have an instance of the Database Engine". Does this also mean that the SSIS server is then redundant if run from a server that does have DB Engine?
You can install SSIS on a dedicated server. It will provide the capability of designing, executing and storing the packages. Packages would be accessible from agent service installed on other server as in your case. I see no issue in this design as per your requirement.
However this design will not use resources on dedicated SSIS server. All execution load will be on calling server with database engine.