@Openmind, it's... complicated but easy.
When it comes to AMP, it's not like a new fast format. Let's consider a webpage of 1mb bult only using html and javascript VS the same version on AMP also with 1mb size. The same megabyte will have to be sent over the internet, same speed, same time, same everything, then it would be about your programming (javascript) efficiency and your browser dealing with both pages. This is given the case of a visitor coming to your site directly via URL, it's the same thing on both cases, no difference. What I'm saying here is, if you are looking for ways to speed up your page/games, AMP is not exactly the solution.
What's the difference with AMP pages? when you visit Google and search something and your site appears on the results, then Google sees you are AMP compliant and then when you click on your result, your page loads like magic, why? because there is a preloading. Your content is being cached/preloaded (any of both) and served from the location nearest to you, then you hit your site but some or all of your stuff was already loded. Bing introduced AMP support, Yahoo did too.
So, it's like someone visiting your site from zero, directly, the browser loads everything from scratch every time. This unless that someone visited the site previously so browser cache enters the game, there you can also play and optimize for cache (via htaccess, meta tags, etc) and make your site load faster, why? because that person already cached some elements in their browser. Ok, when it comes to Google search results, it's like that someone had a friend giving them a copy of your site so when they get to you they already have some elements int their browser, Google is that "friend" giving that copy. Bing and Yahoo can do this too. CloudFlare entered the game and somehow you can be served some cached content too. Tried my best to explain how it works, I too got caught at the beginning into thinking it as a faster format, it's not exactly that. It was bult for preload and cache but not on your browser, instead somewhere else.
About your games, I don't know. I would use Perl. Yes I love Perl but it's not just that, Perl is way good parsing text, but this is server side. I would serve this via AJAX. You can do this with any other language server side. The thing is, you can do it even better with Javascript (word games), the problem is serving the JS means you are also serving the source code of your games, but many people do this without a problem. This is not AMP related. Javascript would be faster meaning evertying is loaded on your browser from scratch when the whole page is loaded. You can do this with AJAX serving the page and then loading the rest but this would mean some extra time.
Yes you can bulid PWA, but that's not AMP. Having a website or an app are two diff things depending on your goals, you mention not wanting to build a native app, well you can build something else: hybrid app. There you can use your html + javascript skills (and communicate with your server if you need to). I've tested many out there (hybrid solutions) my votes go to Telerik and Monaca, both very easy to use with a library of examples and tutorials. PhoneGap can work, iOnic too, but I have my reservations on both, besides they rely only on cli (command line clients), it's up to you. All of them offer free accounts and paid too (they all build Android and iOs).
Good luck.