You're not missing out. After being intrigued by the trailer showing the solo campaign and the pretty cool gameplay and graphics, I bought it Saturday and let it download overnight. Installed it this morning and started it up, but the tutorial crashed. Restarted it (remap the keys again because it didn't save them) and launched the campaign mode . . . which is online and multiplayer only. WTF?
Apparently, "campaign mode" now means "goal-oriented multiplayer modes with no story" like conquest while "classic mode" means "standard multiplayer games with no story" such as team deathmatch or capture-the-flag.
Twenty-four hour return policy activated, and good riddance. You'd think with all the cash EA has they could produce an online store half as good as Steam (much as that raises ire for some people), but alas that is not the case.
BTW, that browser extension was the server browser. I have no idea what it bought them to write a bunch of C code in a browser extension rather than packaging it up into a regular executable, but the major downside is that every time you join a server the entire engine has to be loaded and initialized. If these were the good ol' days of 2 second startup times it would be no problem. I gave up on BF4 pretty quick as it got so tiresome waiting for the game to reload every time you switched servers.