Which device (not software) does Khan Academy use to write?

Its called a stylus.

In computing, a stylus (or stylus pen) is a small pen-shaped instrument that is used to input commands to a computer screen, mobile device or graphics tablet. With touchscreen devices, a user places a stylus on the surface of the screen to draw or make selections by tapping the stylus on the screen.

Pen-like input devices which are larger than a stylus, and offer increased functionality such as programmable buttons, pressure sensitivity and electronic erasers, are often known as digital pens.

The stylus is the primary input device for personal digital assistants. It is used on the Nintendo DS, Nintendo 3DS game consoles and the Wii U's Wii U GamePad. Some smartphones, such as Windows Mobile phones, require a stylus for accurate input.[3] However, devices featuring multi-touch finger-input are becoming more popular than stylus-driven devices in the smartphone market; capacitive styli, different from standard styli, can be used for these finger-touch devices (iPhone, etc.).

Graphics tablets use styli containing circuitry (powered by battery or operating passively by change of inductance), to allow multi-function buttons on the barrel of the pen or stylus to transmit user actions to the tablet. Some (probably most) tablets detect varying degrees of pressure sensitivity, e.g. for use in a drawing program to vary line thickness or color density.

The first use of a stylus pen in a computing device was the Styalator, demonstrated by Tom Dimond in 1957.

Khan Academy Writing