Do I need a graphics tablet to use MyPaint?

No. You can use a mouse or a touchpad, but a graphics tablet is very highly recommended for drawing. Graphics tablets have much higher resolution than simpler input devices no matter that the make.

The practical result of this is that you will get somewhat blocker lines if you use a mouse when zoomed out a lot.

Try turning up the “slow position tracking” brush setting to compensate for this if you see lots of straight lines at multiples of 45° and 90°.