There are two parts to this question; the genre (multiplayer), and the technology (browser-based).

Let me talk about the technology first.

We are already there. With notable games on store shelves that are purely reliant on web technologies (Cross Code, and Elliot Quest - written using impact.js - are my favourites from the lot); it is not the future anymore.

Back in 2014, Mozilla announced asm.js; in collaboration with Humble Bundle. They opted to test this technology to get a few famous indie games running on the browser. Here is the catch, these games were not written for the browser; the source written in C/C++ was compiled to be run as a web application on Firefox. Also, asm.js is the basis for the newly announced WebAssembly standard.

The take away from all of this is: the future is looking really bright on the browser side, for game development; not only because there exist awesome technologies which enable you to write games for the browser; but also because of the awesomeness of a bunch of developers who have taken it upon them to bring the efficiency of low-level languages like C/C++, to the browser (asm.js, back when I read about it was only 2x slower than your traditional C compiler).

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I'm hugely passionate when it comes to games, and games as an art form; so I will also answer the genre part of the question for the sake of completeness, for my sake. :D You can safely skip this.

Slither.io is definitely an interesting game, and sure, we might see a lot of real-time multiplayers like this, in the days ahead; but they will only be a part of the lot. Just as EDM (it is in trend right now, I hear) is not going to be the future of music; so is the case with the answer for this part of your question.

Let me give you my perspective. At a bird's eye view, I see the current game dev. scenario infused with a lot of brilliant indie developers coming out with games that have a high amount of contemplative content; and with stories that have strong emotional anchors. In this regard, computer games are but an art form that go alongside with their older siblings: movies, books, and music. Off the top of my head; The Swapper, Braid, Fez; are a few such games, that I highly recommend, if you want to explore.

As one game designer has aptly put it:

"Game designers are obsessed with emotion. How do we create the emotions that we want gamers to feel, and how can we really make it this intense, emotional experience?" - Jane McGonigal

Well, I see that there is a trend of making everything browser based so, yeah, why not, althogh I think we are a long way from that.

haha, so funny game :)) I believe we can do everything in web browser. The biggest challenge is performance.