Thanks again! Yeah, I tried the game out on another computer with a Retina screen, and sure enough, I had the same issue. Bah. I haven't spent much time making UIs in Unity so I don't know if there is an easy solution for this, like some checkbox I didn't check or something. But it's good to be aware of the issue.
All I did to map the UI onscreen was to create a Canvas, add several text components inside, then use the anchor/pivot settings on each one to position them in the lower-left corner of the screen (or lower-right in the case of SPACE), and then tweak their x and y coordinates. I don't know why that positioning would be thrown off by a different screen resolution/density. My best guess is that the Canvas itself has a size/resolution and relative position to the rest of the game screen that is affected by the display in question. Will have to do some research.
You're right that it's more inconvenient to have to look at the corners of the screen than wherever the player is, but that was actually my intention. I hoped that would add to the funny, frantic, out-of-control feeling I was going for, sort of similar to the concept of the Wii U game ZombiU, where you have to look between the zombies closing in on the TV and your items on the GamePad in real time. But I take your point—the application may be different enough here that it doesn't really work.
I appreciate the kudos and all the feedback!