A gyro-stabilized thing like this is usually more stable than a three our four-wheeled one, which can't fight back it's own weight.
Products like the Headthere Giraffe have a heavy-ass base full of batteries so the centre of gravity is lower than an office swivel chair. Which of course keeps it stable even if the battery runs down or the software crashes.
It's not a very elegant design, though, and it makes carrying the thing a hassle.