i like to imagine fan themes i hear as alternate universes, with this being one where the reboot started in 2000, with the thing before the first episode being "The Doctor is back for the turn of the millenium, where he has to face a potentially world-ending computer bug."
Definitely going to use this in my D&D campaign. A punky theme for an inventor, willing to help the party. I'm going to talk over it, not saying much about Doctor Who. The hints are all in the music if you listen well, but it's not obvious. Then later, I will reveal his secret life project: a time machine. I play the same music louder, and be quiet. The big reveal, but it was there all along in the background music. If you just listened.
The melody is making me think a little bit of the Dimensions in Time theme. Regardless of how cringe that theme may or may not be, your rendition of the theme tune here is quite a head bob! Definitely not a "mainstream" arrangement, but it's great on it's own terms!