How to process output of a i2c sensor to get proper values.

Assuming that's a TI TMP117 (providing a link to the chip and / or the library you try to port sometimes helps, or saves a couple of seconds), the Arduino code simply reads two bytes from register 0.

At line 17 that delay

  // Delay to allow sufficient conversion time
  delay(10); 

I don't think its necessary for two reasons:

1. the datasheet doesn't say it's necessary :) (If I read the datasheet correctly, in continuous mode - and that's the default - you can just read the temperature values. Maybe you would have to wait before the first, but see the second point:
   
2. Espruino is slow, so usually you can just ignore < 1ms delays. :) But always test it...
   
   

I think @maze1980 is pretty close, this probably works:

var addr = 0x48; //chip addr
read = function(reg, len) {
  i2c.writeTo(addr, reg);
  return i2c.readFrom(addr, len);
};
write = function(reg, data) {
  i2c.writeTo(addr, [reg, data]);
};

// read two bytes from register `0`
var b = read(0, 2));
// and calculate the temperature:
var temperature = ((b[0] << 8) | b[1]) * 0.0078125; 
console.log('temperature:', temperature );