Well, this is a matter of debate and quite careful deliberation.
You can use the JTAPI JAR files for developing a web application. That is supported.
Please see the FAQ "Can the JTAPI SDK be used for developing Web-based applications?" at
https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/support/faq/jtapi/index.gsp
But then developing an application similar to Agent View sample application especially when you need screen-pop functionality is not going to be very straight forward.
The Web Applications work on request-response model. Your web application has to seek response from server.
Now applications like Agent View, they need to get event updates. So to do that in a web application means that you have to keep polling for events very-very frequently e.g. keep refreshing the browser... and that's not very practical.
Other options are to consider long polling or server push mechanisms available.
As I said, it's going to need deliberation.
Regards,
Mak