Hey 4ian,
First of all I understand why moving to a web based app is a tempting option. You don’t have to code and test for different platform for each release which would give you more time to fix bugs and add new features. 
But my past experiences with Web apps have not always been that great. I use Goolge Docs almost exclusively, I don’t even have a word processor installed on my computer which on one hand is nice but in the event of internet failures I feel helpless.
I’ve tried using Pixlr which is slow and tedious compared a native graphic editor. An excellent app that I like to use is webchemy but again a simple chrome crash can spoil hours of work and if i’m not connected i can’t load the app. Also, and this may be exclusively for me but working on a browser is a distracting affair. I often find my self wandering to different sites.
And though each page runs as a different process i have faced global unresponsiveness issues due to some page error.
That aside I think that you should pursue a web app if you feel like it. As a community member I would love to see it flourish but I also think that improving the native version is a better option.
I downloaded construct 2 and Game develop at the same time. But as pointed out lack of tutorials, written and video are a major set back. In the past months I’ve managed to learn and have created 2 games in my free time using construct but trying to do the same in Game develop is more challenging.
I agree GD needs unique features but as I remember it did have them. Remember GD had lighting way back before whereas Construct only added it in this release. Also native support desktop.
I think GD should move with adding and improving the native version before venturing of to a Web based app.
though this is not the place or time but here are some things I think that can really boost up GD reputation
Features
–You must have heard of the game dev community’s demand for Ubisoft to release the UbiArt engine, why not implement feature like that into GD.
–Simple track animation combined with event based system would really attract a lot of developers. The ability to create cutscene will automatically boost the engines appeal and help create more polished games.
–Also, I’m sure people would jump on the opportunity to use an engine that support Vector Graphics. That hasn’t been done yet.
–Features like internal support for skeletal animation would be welcoming as suggested by others.
–Adding native export for android is also bound to make people consider game develop, and will also help it surpass Construct’s current feature set. (adding support via wrappers are not always successful.)
–I think GD have one of better UI’s then some of its competitors and it can be further simplified like the event sheet and naming.
I know it’s more easier said than done but having them in your agenda and promoting the upcoming features will make us look forward to new releases.
Tutorial
–It would be a great start for beginners if you have a small video series with a even 2-3 episode, one explaining the UI and another, hour long, on how to create simple game clones like that of Mario (complete with design, score, enemy AI, sound and export) and/or a simpler, faster Flappy bird.
Investing a week on a project like this will definitely ease up new users.
Marketing
–Being more active on Twitter and Facebook like other competitors will help a lot and though it might be not possible for one man to do all of it, you can ask a friend to be your Social Media Manager (people like designations). 
–Constantly indulging users to request new features, choose between new projects and also to report bugs and UX hurdles.
–Stressing on “Free Engine” and “Multi-Platform”.
Also I want to add that I was really happy for the Crowd funding initiative and though I couldn’t contribute I tried my best to spread the work on Twitter, FB, and Reddit’s gamedev community (where they politely told me I cannot promote a crowd funding if i’m not associated with the company/project, but they did say they would be glad if you did it yourself.)
Sorry for the lengthy post and going beyond the scope of the topic but i think if these issues are addressed properly first it would create a good platform for a future web based venture.
Also find a simple two syllable name that should be priority one (even if you go forward with a Web App idea).