PyJS | A minimal Python interpreter written in JavaScript | Interpreter library

Pygame will be of no use to you here. You could probably do it (sockets won't be very useful to you either) I don't suggest it though.

If you learned JavaScript you would find your task much easier. Creating a game would require a canvas and that is JavaScript's specialty, even the web-frameworks such as Flask and Django don't inplament them, so eventually you will probably find yourself writing a lot of JavaScript anyway, games are very complex sooner or later your will find some hitch that will not be inplamented and will be forced into writing JS anyway.

Then you would probably need logins or a way to save scores. This is where Python can be useful, you could send all the information to be processed server-side in Python. This has been done before and is reasonably easy.

If you are talking about a 3d game don't, you will need some form of 3d engine such as three.js, those will be coded in JS (you will find all online engines are inplamented in either JS or Jquery) and those will cause endless headaches if you try to use one of those in Python.

If you want to develop an online in-browser game you will need to know some JavaScript knowledge at some point or another, Python is excellent server-side and good client-side as well, however games are extremely complex at the best of times with graphics and all. It is not like a web-page, this is an enormous task to undertake (even armed with all the web-development languages -HTML/CSS/JS/Jquery/AJAX/SQL/AngularJS this is an enormous undertaking), and using Python just makes you task much much more difficult, you will go though a lot of hassle and in the end, if you ever do survive it, it would probably have been easier to learn JS and use that.

Server-side, yes go for Python, if it is client side you need JavaScript.

If you still decide to do this start with a simple 2d single player game like flappy bird or tetris and then progress to something harder.