In this video, what is the instrument played by the girl (on the far right)? It’s a string instrument that seems to be something like a ukulele or small guitar, but having a triangular body.
Looks like it might be one of these:
Could be a balalaika but the soundbox doesn’t look that big.
What is the name of that humongous guitar, I wonder?
Nah - I agree it is a Strumstick - which at first glance appears to be a glorified Martin Backpacker* that is played in an open tuning to make it super easy to pick up, or something like that.
*Martin Backpackers are what they sound like - a camping guitar. They are shaped like that with a somewhat shorter neck, and to my ears, they sound frickin’ awful. But if you need music for whatever reason hiking into woods, they are the way to go.
It is a stick dulcimer – a form of Appalachian Mountain Lap Dulcimer arranged to be held more like a guitar. There are several brands available, Strumstick is one, but many are home made, often from kits.
The dulcimer is probably the easiest musical instrument to play.
An explanation of stick dulcimers.
The video that got me interested in playing dulcimer several years ago: Julie Ann Johnson on mountain dulcimer - YouTube
Seagull has a nice 4 string dulcimer similar to the strum stick.
Thanks, all!
BrainGlutton, the giant guitar is something the band got at a pawn shop a while back, if I remember correctly. I think it’s just called a guitar. 
I’ll second that it’s not a balalaika. I’ve got one, and it’s the piccolo balalaika, the smallest one, so I can tell you that as they change size, they scale up or down; the proportions don’t change.
Based on that vid, “drum” would be a better name.