You'll have to ask the app/plugin creator/distributor, perhaps there's a parameter to modify so that the port number isn't added.
> Is there a way to allow this type of URL: 'http://localhost:8080/example-site'
Yes, but you need to tell Apache to listen on port 8080, so as mentioned above :
If, in Wampserver, you want to use ports other than 80, you must create these additional ports by Right-Click -> Tools -> Add a Listen port to Apache.
Your local sites must be defined as VirtualHost, where you can set a specific port for this VirtualHost and the call will then be: 'http://example-site:8080/'.
See :
The need for Virtual Hostand :
Wampserver 3 - Create or add a VirtualHost---------------------------------------------------------------
Documentation Apache -
Documentation PHP -
Documentation MySQL -
Wampserver install files & addons