A website with pictures, an embedded video and downloadable 32bit Windows exes or perhaps an Android APK* of the game is usually your best bet.
This also has the added benefit of letting your viewers get a local copy of your game to pass around so not having to worry about internet streaming which is quite a benefit (whereas many web games need internet or a small local html server (like mongoosehttpd) to be provided). Or even worse, they need horrible web plugins**!

With Python, you might want to use a packaging system since Python isn't very common on Windows machines for a typical user. If you can modify your install of python to be portable, then you might have some luck creating a self extracting .exe using WinRAR.

Emscripten (C/C++ to Javascript) compiler can compile a Python interpreter so depending on what dependencies your game uses, you might be able to get it running on a webpage too.

* Android is the most common tablet OS (rivaling even that of desktop systems) and seeing as you are not trying to sell your showcase game (at this point in time) your viewers can sideload it without the faff of developer certificates from something like iOS or Metro.

** I am looking at you, Unity web player! Though the developers are currently working on a WebGL javascript exporter using Emscripten.

If you want a playable browser demo using pygame, I can't think of how that would work.

Given your target is web, you should consider HTML5, Java Applets or Unity (bulky plugin tho), instead of python.

If you already have the game, but you only want to showcase it, try making a gameplay trailer and posting it along with a download link for an exe demo somewhere.

In that case, there's probably no way to do it using pygame. Pygame is a wrapper for SDL, and I don't think SDL can be embedded into a web page.

The following example shows an SDL (C++) program compiled using Emscripten to run on a web page.

http://mutiny3d.org/doku.php?id=demos:postprocessing

It can be done, the question is if the python interpreter (when compiled via Emscripten) can utilize the port of SDL. For this you might want to ask on the Emscripten mailing lists.

Youtube videos get many views if the title of the video is chosen carefully. Windows movie maker works well and easy to learn in my opinion. There are tutorials on how to make Youtube videos and upload them. Many game developers use this as a hook and provide a link to a demo website under the video in the description. It is wise to have a demo version of the game and let them have at it. If they like it enough then they will want the full version. Standards are 5 or 10 minutes of play in many cases. So look for host websites for games.