According to Wikipedia, a web application is:
Any application that uses a web browser as a client. The term may also
mean a computer software application that is coded in a
with a browser-rendered markup language like HTML) and reliant on a
common web browser to render the application executable.
Since this matches the description of your web application, I don't see why you couldn't use Schema.org's WebApplication for web applications.
According to Google's docs on rich snippets for software applications, you should likely include the
browsers property to describe the browser requirements, for example: "Browser required with HTML5 and JavavaScript support".