You’ve definitely got the gist of it. I’m hearing the following differences:
1. Your white noise is much louder. I’d back off a bit
2. Their lead is big, wide and wet. Yours sounds narrow. Try applying some Unison with a lot of width but not a ton of detune, and crank up the reverb on it
3. Their overall mix is brighter and compressed. Try adding EQ and compression after all of the layers.