Specifically, does a character killed by the necrotic damage from the energy drain of certain undead creatures (i.e. a wight) but not the reduction in maximum hit points rise as a zombie?
If the life drain attack kills them, they rise as a zombie
The life drain attack of the Wight says:
A humanoid slain by this attack rises 24 hours later as a zombie under the wight's control, unless the humanoid is restored to life or its body is destroyed.
The attack deals necrotic damage and additionally lowers the hit point maximum if the target fails its Constitution safe.
There is no condition that states the target would only raise as a zombie if they die due to their HP maximum being reduced to 0. The term "this attack" refers to the life drain attack in its entirety. It is sufficient if they die from the attack's necrotic damage.