Can AMP be used as both mobile and desktop versions?
I think it is possible to use AMP in web or what you said desktop. The purpose of AMP is for creating fast-loading mobile web pages, but this is not mean that it is only limited for the mobile.
If you also check the Supporter browsers part in this Github, It is stated that:
In general, we support the 2 latest versions of major browsers like Chrome, Firefox, Edge, Safari and Opera. We support desktop, phone, tablet and the web view version of these respective browsers.
Beyond that the core AMP library and built-in elements should aim for very wide browser support and we accept fixes for all browsers with market share greater than 1 percent.
For more information about AMP, check this page and the link that you provide in your question.
It is possible, your site is going to work well on both Desktop and Mobile devices, it's going to load properly and work really fast.
BUT, keep in mind that AMP is more oriented toward mobile devices, all of the current libraries that you can use are definitely focused in creating a faster experience on small devices, and some of the mayor sites implementing AMP are using different version, like Mobile, Desktop and AMP version of each page or article, sounds complicated to maintain, but it allows to offer the best experience for each user on every device.
So, if you want to create a cross device site from start, AMP is a good option, just keep in mind that a bunch of the things you see on other sites (interaction plugins, javascript libraries, complex ajax functionality, complex forms and validations) are not currently supported, maybe in the future, maybe not.
I have created a completely new AMP-only website from scratch, and after around 6 months it is well indexed in Google search engine and getting consistent traffic. It works perfectly on all platforms - Mobile, Desktop as well as Tablets. (By AMP-only website, I mean there is only one version which is AMP. There is no other separate version for desktop, and the same AMP version is shown on all devices.)
However, after months of hard-work, I found the following shortcomings with this AMP-only approach:
A lot of functionality and features are unavailable in AMP (like those which can be easily accomplished through JavaScript), and we have to make a lot of compromises which takes a toll on end-user experience.
Even simple looking features which can be easily implemented in a non-AMP site (like form submissions) needs a lot of work to make them AMP-compatible and still the desired may not be accomplished fully.
Worst of the lot is when it comes to monetization. I was under the impression that since AMP is Google-supported, adsense implementation will be a cake-walk. But got a nasty surprise!
3.1) Google's AMP AUTO ads don't work at all. There is absolutely no help available either from Google, its official forums, or anywhere on the net. (Just do a Google Search on "AMP Auto Ads not working" and see if you can spot even a single solution. There are only questions and repeated AMP code snippets which don't work.)
3.2) Google's AMP ads (non-auto ones) also work highly erratically. They don't show up when the site is accessed on a Desktop, and they display only on mobile devices. Its a big loss of revenue for the publisher, despite Google's claim that these ads show seamlessly on all devices! Once in a bluemoon, they may be visible on desktop, but 90% of the times they are not.
3.3) If you try to use other ads (non-Google Adsense), then you will find that most of the ad agencies don't offer AMP-compatible ad display code. Almost all have Javascript code which is non-AMP. So if you use them, AMP benefits go away. At the end, you are solely tied to Google Ads which themselves may/may-not work.
So to summarize the answer to your question ("Can AMP be used as both mobile and desktop versions?") - Yes, it can be, and your site can be well indexed in Google.
But (and its a big but), if you are planning to monetize your site through ads (Google or others), or if you want to give a proper end-user experience to your site visitors, then better to have two separate versions. It appears that AMP remains a Google work-in-progress with loads and loads of issues. It's the publishers who work hard and end up disappointed, so better keep multiple versions.
Above all, there is no help available from anywhere - not even Google. I learnt it the hard way. This question was raised in 2016, and even in 2020 AMP remains a challenge.
Update as of May 2021:
It is better to completely ditch AMP.
AMP is for accelerated mobile pages - i.e.- they are fast pages that are suppose to load quickly on mobile. AMP was launched at a time when mobile networks were slow, and net companies (including Google) were looking for speedy pages that load quickly on mobiles (and their then slow networks).
Fast forward to 2021, 4G and 5G mobile data services are now readily being available across the globe. Now, the benefits of AMP are no longer worth the restrictions AMP imposes.
Each page, whether bulky or light, still loads easily on mobiles because high speed net access is now available on 4G/5G.
So avoid taking a deep and big cut in your site functionality while complying with AMP.
Instead, go for a fully-functional non-AMP website, and keep your site users happy by offering them full functionality (not restricted by AMP).
Thanks!