Is it supported to install SharePoint 2013 on Windows Server 2016?
As a short answer: NO. SharePoint 2013 is NOT supported on Windows Server 2016.
Note: the Windows Server 2016 doesn't have an Application Server Role.
The tool was unable to install Application Server Role, Web Server (IIS) Role
Although it's not supported to install SharePoint 2013 on Windows Server 2016, you still can do it by installing .NetFramework 3.5 as mentioned at Install .NET 3.5 Framework on Windows Server 2012 R2
You can also do the following:
- On your SharePoint Server, Open Windows PowerShell As an administrator.
- Run the below cmdlets one by one
Enable .NetFramework 3.5 on Windows Server 2016 / 2012
Import-Module ServerManager
Add-WindowsFeature NET-WCF-HTTP-Activation45,NET-WCF-TCP-Activation45,NET-WCF-Pipe-Activation45
Add-WindowsFeature Net-Framework-Features,Web-Server,Web-WebServer,Web-Common-Http,Web-Static-Content,Web-Default-Doc,Web-Dir-Browsing,Web-Http-Errors,Web-App-Dev,Web-Asp-Net,Web-Net-Ext,Web-ISAPI-Ext,Web-ISAPI-Filter,Web-Health,Web-Http-Logging,Web-Log-Libraries,Web-Request-Monitor,Web-Http-Tracing,Web-Security,Web-Basic-Auth,Web-Windows-Auth,Web-Filtering,Web-Digest-Auth,Web-Performance,Web-Stat-Compression,Web-Dyn-Compression,Web-Mgmt-Tools,Web-Mgmt-Console,Web-Mgmt-Compat,Web-Metabase,Application-Server,AS-Web-Support,AS-TCP-Port-Sharing,AS-WAS-Support, AS-HTTP-Activation,AS-TCP-Activation,AS-Named-Pipes,AS-Net-Framework,WAS,WAS-Process-Model,WAS-NET-Environment,WAS-Config-APIs,Web-Lgcy-Scripting,Windows-Identity-Foundation,Server-Media-Foundation,Xps-Viewer