The left first. || uses what is called short-circuit evaluation, also known as minimal evaluation, meaning it will only evaluate the right side of the expression, if the left side is false.
From the ECMAScript Language Specification:
11.11. Binary Logical Operators
The production LogicalORExpression : LogicalORExpression ||
  LogicalANDExpression is evaluated as follows:
- Let lref be the result of evaluating LogicalORExpression. 
- Let lval be GetValue(lref). 
- If ToBoolean(lval) is true, return lval.
- Let rref be the result of evaluating LogicalANDExpression.
- Return GetValue(rref).
Thus, in your expression: 
ctx['ballctx'] || createCanvas('game-screen', 'ballctx');
^-- lval          ^-- rval
If lval evaluates to true, rval won't be evaluated. In other words, you'll only create a new canvas if ctx['ballctx'] evaluates to false, so your code is correct.