I'm trying to fathom why that cap is attached in a manner to bridge that surface-mount resistor(?). It's like they're simultaneously throttling power on that pathway, while using the cap like a step-up transformer to spike the power at that point. It's like that overly complicated crappy 'common core' math, they want a different power level at at the other side of that gap but instead of getting there in one move with a resistor OR cap, they are making two moves in opposite value directions to arrive at a sum that gets what they want. Like wanting -1, but instead of subtracting 1 they are adding 5 then subtracting 6.
Like they built that circuit, did the production run, then discovered they'd throttled the power down too much, so the production fix was 'stick a cap on it at R3' to rectify the undervoltage and make the whole thing light up properly.
/typically you can get away with putting LEDs in a serial run, if their combined need is slightly under your input voltage. Their combined draw seems to exceed the available power. So they stick a cap on it to boost the juice enough to get by? When a proper series of lower-value resistors would have been the correct solution. Instead of re-working every resistor, they did it in one move by adding the cap. An efficient manufacturing fix to a poorly designed circuit. All depends how they laid out their circuit(s). Just seems like a hack(ed) layout.
(shrug) as long as it works. But that cap is a failure point. OP, if that light fails in the future, the first thing I'd do is take a look at that cap for typical signs of failure. Might even be wise to get some spares right now, while you have it open and can identify at part number on it.
eta
that's all supposition on my part, and only generally true if that's actually a resistor being bridged by that cap.
