Is it possible to run game made with pygame on browser using pyscript?

No, Pygame is not supported in PyScript at this time. I'm not sure what is the best way to find out what packages are supported, but I have managed to piece together the following:

1. PyScript uses Pyodide to load packages, so only packages supported by Pyodide will be loadable in PyScript. That means either packages built with Pyodide or pure Python packages with wheels available on PyPI or from other URLs.
2. Pygame is not yet supported by Pyodide.

You can use the following test script to see if a package is supported:

<html>
    <head>
      <link rel="stylesheet" href="https://pyscript.net/alpha/pyscript.css" />
      <script defer src="https://pyscript.net/alpha/pyscript.js"></script>
      <py-env>
        - pygame
      </py-env>
    </head>

  <body>
    <h1>PyScript import test script</h1>
    <py-script>
import pygame

    </py-script>
  </body>
</html>

This is basically just a "try it and see what happens" script that will throw an error in the console if a package is not supported. The error you'll see will be

ValueError: Couldn't find a pure Python 3 wheel for 'pygame'. You can use micropip.install(..., keep_going=True) to get a list of all packages with missing wheels.

Yes it's possible but has not been made available because :

pyscript uses pyodide, pyodide is NOT optimized for games but for scientific stack instead and notebooks presentations.

Today, i'd recommand using pygbag https://pypi.org/project/pygbag/ from https://pygame-web.github.io. It uses the same principles applied to pygame coming from Panda3D webgl port using Web Assembly for modern browsers.

( and if you really want to support pyscript tags you could probably find a way ).