Is this just syntactic sugar for ES6?

No, it's more than syntactic sugar. The gory details are buried in §13.6.3.9 CreatePerIterationEnvironment.

How is this working?

If you use that let keyword in the for statement, it will check what names it does bind and then

• create a new lexical environment with those names for a) the initialiser expression b) each iteration (previosly to evaluating the increment expression)
• copy the values from all variables with those names from one to the next environment

Your loop statement for (var i = 0; i < 10; i++) process.nextTick(_ => console.log(i)); desugars to a simple

// omitting braces when they don't introduce a block
var i;
i = 0;
if (i < 10)
    process.nextTick(_ => console.log(i))
    i++;
    if (i < 10)
        process.nextTick(_ => console.log(i))
        i++;
        …

while for (let i = 0; i < 10; i++) process.nextTick(_ => console.log(i)); does "desugar" to the much more complicated

// using braces to explicitly denote block scopes,
// using indentation for control flow
{ let i;
  i = 0;
  __status = {i};
}
{ let {i} = __status;
  if (i < 10)
      process.nextTick(_ => console.log(i))
      __status = {i};
}   { let {i} = __status;
      i++;
      if (i < 10)
          process.nextTick(_ => console.log(i))
          __status = {i};
    }   { let {i} = __status;
          i++;
          …

I found this explanation from Exploring ES6 book the best:

var-declaring a variable in the head of a for loop creates a single binding (storage space) for that variable:

const arr = [];
for (var i=0; i < 3; i++) {
    arr.push(() => i);
}
arr.map(x => x()); // [3,3,3]

Every i in the bodies of the three arrow functions refers to the same binding, which is why they all return the same value.

If you let-declare a variable, a new binding is created for each loop iteration:

const arr = [];
for (let i=0; i < 3; i++) {
    arr.push(() => i);
}

arr.map(x => x()); // [0,1,2]

This time, each i refers to the binding of one specific iteration and preserves the value that was current at that time. Therefore, each arrow function returns a different value.

let introduces block scoping and equivalent binding, much like functions create a scope with closure. I believe the relevant section of the spec is 13.2.1, where the note mentions that let declarations are part of a LexicalBinding and both live within a Lexical Environment. Section 13.2.2 states that var declarations are attached to a VariableEnvironment, rather than a LexicalBinding.

The MDN explanation supports this as well, stating that:

It works by binding zero or more variables in the lexical scope of a single block of code

suggesting that the variables are bound to the block, which varies each iteration requiring a new LexicalBinding (I believe, not 100% on that point), rather than the surrounding Lexical Environment or VariableEnvironment which would be constant for the duration of the call.

In short, when using let, the closure is at the loop body and the variable is different each time, so it must be captured again. When using var, the variable is at the surrounding function, so there is no requirement to reclose and the same reference is passed to each iteration.

Adapting your example to run in the browser:

// prints '10' 10 times
for (var i = 0; i < 10; i++) {
  setTimeout(_ => console.log('var', i), 0);
}

// prints '0' through '9'
for (let i = 0; i < 10; i++) {
  setTimeout(_ => console.log('let', i), 0);
}

certainly shows the latter printing each value. If you look at how Babel transpiles this, it produces:

for (var i = 0; i < 10; i++) {
  setTimeout(function(_) {
    return console.log(i);
  }, 0);
}

var _loop = function(_i) {
  setTimeout(function(_) {
    return console.log(_i);
  }, 0);
};

// prints '0' through '9'
for (var _i = 0; _i < 10; _i++) {
  _loop(_i);
}

Assuming that Babel is fairly conformant, that matches up with my interpretation of the spec.