HES shareholders may be affected by when—and to what degree—John Hess and other family members decide to monetize a significant chunk of their HES stock. This, in turn, is affected to some degree by changes to the capital-gains tax and the death tax (a/k/a estate tax).
Note that the federal death tax is in addition to the 16% death tax levied by NY State (John Hess' tax domicile), so the top Federal+NYS death-tax rate under HRC's proposal is ~71% compared to ~50% under the existing tax code.