Wasn't able to find a video of the app working, but did find this Javascript port (?), and it seems to roughly match the appearance shown in screenshots:
This is not rule.
Some planes named "friendly to novice pilot", and are stable, others are not, and this is somewhere predictable when design.
I even hear, Lindsberg, when was preparing for his flight, asked designer to make his plane unstable, because typical stable flight is very boring and he scared to fall asleep.
In other cases, modern planes like 737s and larger scale, usually considered to have zero stabilization in design and if need, stabilization created by electronics (navigation system is usually made as very high precision inertial platform, so could in most cases know, how should fly to looking stable). This is because design stabilization costs additional resistance, less payload and more fuel consumption - for 737 scale it is about 1-3 additional passengers and few percents of range. Military planes and some aerobatics now are designed unstable for better maneuverability.
I don't say, this new trends are good, just notice.