The app is only needed for a couple features of voice chat like push to talk when Discord is in the background unfocused.

Server owners are able to configure a verification level. When on the lowest verification level (which is the default setting when making a server) new users without a discord account can join by simply typing the nickname they would like to use.

Unless this is a new thing, I used to do video and audio calls on Discord on Firefox on Linux without issues. No app.