In other words, it seems dishonest for me to claim that I supported
growth among a certain market by building a widget, when building the
widget was not my idea.
You are not being asked only which of your ideas contributed to growing the market. Rather, you are also being asked what you did to support growing the market. If the widget you were told to build did that, you should mention it - that's evidence of support.
How am I supposed to approach this? Is it really just a matter of
drawing lines from my activities to strategic priorities, no matter
how disconnected they are?
You should draw lines from whatever you did to whatever your company's goals/missions/priorities might be. The lines need not be direct at all, nor do the lines need to be "heavy".
The theory behind of all of this is that the company's overall mission and strategic business priorities are conveyed from on high to the next level down. That level then breaks them down into actionable items and conveys them to the next level down. And so on.
In theory at the end of the year each level could indicate the tasks accomplished that helped achieve the overall mission/priorities. And the company could feel good about itself.
In reality, you can only do so much. You must work on whatever is assigned to you specifically. You can pretty much never choose to ignore your assigned work and do something else that you feel better supports company priorities.
So the game at this point is to connect as many dots as you possibly can.
It might seem silly at first, but after a little while you'll get the hang of it. Your widget helped the company be more efficient in their mission, perhaps. The reports you provided helped the company tune its priorities. The meetings you attended helped set direction for others in achieving their part of the company goals. Yes, it's a bit of a game - don't be afraid to brag and exaggerate a bit. But that's the way these "self appraisal" portions of performance reviews go.