These are definitely triplet subdivisions, not duple 32nds. With experience, you can tell the difference even at fast tempos like this.
If I was doing this transcription, however, I would take a very different approach. I would either write in swing 8ths, 4/4 at q=206, or I would keep the meter the same and make a note up at the top indicating "swing 16ths", and then not write a single triplet or 32nd note.
This style of rhythm is right out of jazz music, and the matching notation is rarely explicit about the triplet subdivision that is implied in swing rhythms. You would only write an explicit triplet if you had a note starting on the second of three subdivisions.
One additional tip about your transcription -- the two consecutive dotted 8ths you have in bar 2 would not usually be considered correct. Often it's debatable, but in this case, the second note does actually have a swing placement, and so showing the distinct 16th is important. (If you listen closely, those two notes are NOT the same length!)