Did you update the pg_hba.config file? This file allows the Postgres DB to accept connections from other machines.
You can install PGAdmin or other PG SQL client and try to connect to the DB as the PG Admin?
I think that may have to do with the DB name. The issue may be with the underscore "_" Here is the note from the help:
Type the database name in lowercase; upper- and mixed-case object names are not supported for geodatabases in PostgreSQL. If you type a database name in upper or mixed case, ArcGIS converts it to lower case.
This is step #5 under "Create a geodatabase" at the link above.
Can you please try and create a default DB called "esritest"? and report the results?
Here is another piece of help doc that supports the "_" not being a good thing:
Database management systems have different definitions of acceptable characters for object names. Most names must begin with a letter and cannot contain spaces, backslashes, or reserved database management system keywords. Some databases allow special characters such as forward slashes (/), underscores (_), dollar signs ($), dashes (-), dots (.), or mixed cases. Sometimes the database allows you to use special characters or reserved keywords, or force mixed, upper-, or lowercase names if you provide the object name enclosed in delimiters, such as double quotation marks.
However, ArcGIS does not delimit object names. Do not create any tables, feature classes, indexes, databases, users*, roles, or other object names that require delimiters if you will be using them with ArcGIS. The object will be created in the database, but you cannot access it from ArcGIS.
It looks like in the tool inputs you have the default Postgres port 5432 specified as the Instance name input- is this valid per your configuration? There should be no need to specify the port number if Postgres is running on the default port 5432. If you have a running instance / service on the Windows server- try inputting the name of the database instance (might be the server name if you're unsure) and see if that works. Hope this is helpful!