Hydra had Howard and Maria Stark assassinated in order to get their hands on a new version of the Super Soldier Serum.
As interesting a call-back as that would have been, the deaths of Howard and Maria Stark have nothing to do with Obidiah Stane and his thirst for power within Stark Industries.
Instead, as with a startling amount of things in the Marvel Cinematic Universe, this all ties back into the loss of the Super Soldier Serum after Steve Rogers successfully underwent the procedure. You'll remember that after Bucky has killed Howard and Maria Stark, he retrieves a number of sachets containing a blue liquid from the trunk of the car.
Here is a reminder of what those sachets looked like:
For reference, here is a picture of what the Super Soldier Serum from Captain America: The First Avenger looked like:
The liquid in the sachets that Bucky was sent to retrieve was a new version of the Super Soldier Serum, and was used by Hydra to create "the other Winter Soldiers" glimpsed at in Captain America: Civil War.