To quote the top comment in that video: Vader didn't come here. Anakin did.
Vader(Anakin) was always in conflict with his attachments to his loved ones, and this is another example. His Sith self probably sees her as another Jedi, and his Jedi self sees her as his former Padawan.
If you have followed the events of the Original Trilogy, you can see that even after 20+ years, Vader did not want to kill Luke (Luke was about 22 years old in Empire Strikes Back). He could have easily got rid of him forever at the end of Empire Strikes Back ("No, I'm your father" scene). Luke had his arm cut off and was at Vader's mercy, and still Vader tried to convince Luke to join his side. True, he was merciless when dealing with common Rebels. But he cared for his son. He did not want to lose him.
If you analyze the character of Anakin, he was always conflicted with his emotions and attachments towards others. If we consider the Prequels era, on one hand, there's his mother and a few close friends. On the other hand, the Jedi code which discouraged keeping attachments. He lost most of the ones he was close to;his mother died and so did Padme.Obi-Wan left him to die on Mustafar, probably ending their friendship once and for all. Then there's Ahsoka, his former Padawan. They shared a close bond for many years before falling apart. After losing his mother, Padme and Obi-Wan, his closest to a friend was Ahsoka.
Therefore, he probably wanted to meet his old friend once more. Highly unlikely he wanted to kill her at all.
Also,
If Ahsoka was indeed a threat to the Empire, stormtroopers or inquisitors could finish her off.
I suppose you are talking about Clone-Troopers (even that wouldn't be easy), because Stormtroopers would stand no chance against someone like Ahsoka. She had fought Darth Maul and survived. Do not underestimate her.