A 16% YOY decline is large, particularly since it was declining from an unimpressive number. It's not something to be minimized with the qualifier "only".
I find the idea that there's a large cohort of people who a) want a dedicated handheld, b) look down their noses at the 2DS and c) are deterred by twenty bucks really far fetched.
If a 16% decline is 'large', why wouldn't a 13% price cut not be 'large'? It also doesn't need to convince hordes of people. They only need to convince another 10% or 20% of people. It also doesn't need to make a big impact on peoples thoughts. People on the fence, people 90% convinced but not quite. Price goes down and they cross the line of the buying decision. Just give them that 10% boost in motivation to get the system.