What you are looking for is Khan Academy. Khan Academy with enough content, with sufficiently
rigorous content, with sufficiently rigorous
evaluation, to become accredited so that employers will value their assessment of a students worth. Actually, they would need to be
better than merely being accredited, since employers sure aren't bending over backwards to pay accredited universities serious cash for access to their students.
See, what is Khan Academy really lacking at this point? Is the hard part their website with youtube hosted videos? Are they really just jonesing for some mobile developers? Or is producing quality content with broad coverage and depth their bottleneck?
Making an app is the easy part. Education is not failing for want of an app. Certainly not for want of a gamified app.
But hey, I can't stop you. Knock yourself out. Hell, pitch it to YC; I hear they are doing non-profits now.