Well I try to give a bit more specific feedback/feelings. Salt. Cents. Blaablaa.
First on entering the site, I get this big banner on the top which says things like "SQUASHIES WORLD", "ECHOES+", etc. On first arrival and quick glance I get the feeling I have arrived on some website of company promoting such products (games). Not a website of a company/toolkit for designing such games and just using these games as a means to promote what can be done with it. I would start with a banner on what AppGameKit is, then a bit lower show this one with a title such as "Examples of Games made with AGK" or maybe "Showcase: Made with AGK". This would then link to the showcase tab, which I only just noticed exists as well.
I wouldn't necessarily call AppGameKit a "scripting system". Makes it sound more like game creator where you drag and drop and then script something. Not sure what is a good wording though, balancing between not making it sound too complex for newbies vs overly simplified and giving the wrong expectations.
Coding vs programming in terminology. Not sure how I feel about this. These always get to me as overly simplifying both the task and the people doing it. But then again they seem trendy. Maybe Game Programming Environment. If you want to focus on games. I think that is what AppGameKit is best for given its various properties, but you run the business and probably have a better view/your own ideas.
The title on AppGameKit - perfect all round coding tool in general is a bit off for me. The list below it with the different colored ribbons actually lists your target audiences. Maybe you could word the title there along those lines. The tab for this seems to be "users" so you already have the idea there.
Reach your audience - I think what you put under this is more about "write once, deploy everywhere". Yes, a beat up phrase, shouldnt use it, but just trying to give an idea that reaching your audience is different from what this section promotes. It is definitely one of the best assets of AppGameKit to be able to deploy on several platforms easily and conveniently. Including the AppGameKit player,which makes testing on mobile while developing on PC a breeze. So just saying maybe consider this differently. And here an animation on the phone/background to show development on PC and deployment on Android/IOS would be nice. Whatever would be the sexiest way to show this off as. I would suggest to make this benefit as clear as possible, while keeping it simple. Tough but but.
You could also stick a reference section somewhere with the most awesome quotes from your customers. With fancy sounding titles, what they really feel like having achieved with it, etc. Maybe pick some from competitions you have run or whatever. A few of these actually seem to be on the "users" tab, but they are not so clear on how to access them (click on the small dots).
Also, I think most modern websites don't have such clearly separated top navbar, so I only figured to go there after accidentally mouse-overing the "beginners" and other similar texts. Maybe this could be more clearly shown that there are links on each section to other parts with more info.
Links to web (HTML) demo versions of some selected games might be of interest. For example, the background of the "perfect all round coding tool" could be used separately and link to HTML versions of app store releases from the images.
The "beginners" part on "users" could state more that the code to show the balloon and build the animation and make it happen is really all there. Optimally let the user modify and click run but lets not go too far.
You could host the game examples on github or whatever and link to the hobbyist section as some examples. Or as some tutorials on what they do to show the ease.
The indie section, is the signal image showing the broadcast functionlity? could be useful to explain otherwise it is unclear.
Education, maybe show or link your eduguru app or something?
Features page:
Maybe something a bit more exiting to show than a small circular image? For example what can you do with 2D sprites, what can you do with 3D, physics, ... Small animations with examples?
Here you are with the scripting again, maybe it is OK i dunno.
Plugins. So can I write a plugin in AppGameKit BASIC? And is AppGameKit BASIC same as AppGameKit scripting? How will the user link these? And if I can write a plugin in basic (run it on all IDE platforms?), where are the docs? Got some sexy example plugins?
Command set list is nice. Look I can say something positive, whooppee.
I guess frantic also applies to overall navigation. I would like to see the frontpage as promoting the sub-tabs in a clear manner. Now that I realized you have such ones completely separate from the landing page.
about page:
"go native" does not really clearly tell me what this means. I guess you are trying to say you can also go low level and code at C++ while calling the AppGameKit libs. is this really "native" or just "go low"

? And this section does not clearly tell it is an option vs the scriptiong/basic language whatever you call it now.
well, i already made a mess of my comments by getting lost in the navigation of the site and finding half the stuff there somewhere but not clearly figuring how and where from the front page. so generally take what you might find useful here for some ideas or whatever.