I do think there are some interesting tidbits here, (albeit none of them exactly new), only that OP does not explicitly highlight them. The article is simply a narrative of their success story, with most of the analysis being left up to the reader.

That being said, what I got from it was:

1. Acute Observation. They had a prior product (a tiny social network), and they noticed that one of the features they had implemented (experimentally, I expect), namely the photo-filters, was disproportionally popular among their user base. This is a prime example of what Drucker calls "unexpected success", and drawing lessons from that.

2. Focus. Their original product had a much broader scope and they narrowed it down considerably. Not only did they discard a lot of their existing feature-set, but they also reduced the platform support in order to launch earlier, and test their idea ASAP.

3. Traction Can Carry. They had an existing user base, albeit small, and they managed to cross-sell some of those users on their new product from the start, using them as beta testers. This is similar to the "halo effect", only on a much smaller scale.

4. Luck. As OP puts it: "[Our] combination of being photos-first and public-by-default would prove to be a combination that solved an unmet need."[1] I suppose they thought this through, but as far as turning out to be right, I suppose one could say they got lucky.

The take-away for me then is that we could try to observe "unexpected success" of experimental features in our own, or even other people's products, and use the same strategy of applying focus; and that in the end there is always an element of chance, so one needs to keep trying different things, or different variations of the same thing, until one gets it right.

[1] Someone else mentioned Radar.net as a precursor to Instagram; but that app did not have the feature of being public-by-default.