They index them with doubles, they do the same with loop variables. As long as your integer is less (in absolute value) than about 2^53 (because they have 53 bit mantisas) you can represent it exactly with a double. 2^53 is 2^(10*5+3) so even if you're indexing individual bytes that many indexes works until you need to index into an array with 8 petabytes of data in it, at which point you're probably not using javascript anymore.

Like many things in javascript it's a bit cursed but it does work.

In practice, JavaScript has 32-bit signed integers and 64-bit floating-point numbers as distinct types (look into any JS engine, and you'll see a distinction between the two being made), even if they both surface as a single "number" type. You can also see the distinction in the way that bitwise operators coerce numbers to integers, even though the arithmetic operators coerce to floats in theory.