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It's good that you use === and !== for (in)equality checks!

You can use Object.assign instead of your custom extend() function: opts = Object.assign({}, defaults, options || {}). Be aware, though, that it cannot deep-copy/merge!

I got into the habit of declaring every variable either with let or const and never with var. In 99% of the cases, you really want block-scoped and not function-scoped variables.

Especially, I would recommend against declaring your helper functions as var getMousePos = function(evt) {. This way, the variables could even be reassigned, which is almost always a strange behavior for functions.
Either write const getMouePos = function(evt) { or function getMouePos(evt).

Use consistent string quotes: either '...' or "...", but not both if not required (e.g. const str = "Eve's dog is barking").

The code repeatedly makes unnecessary function calls: draw(getTouchPos(e).x, getTouchPos(e).y). Granted, they are probably super cheap in your case, but could be avoided even without doind any kind of premature optimization:

Make draw accept a {x, y} object. If you now also replace startX, startY by a single variable, this would make the internal API much more consistent.

Introduce a variable:

 // Previously draw(getTouchPos(e).x, getTouchPos(e).y); // Now const touchPos = getTouchPos(e); draw(touchPos.x, touchPos.y); // Previously startX = getTouchPos(e).x; startY = getTouchPos(e).y; // Now const touchPos = getTouchPos(e); [startX, startY] = [touchPos.x, touchPos.y]; // or arguably with two lines