I remember looking at Inferno in Heroes 3 and immediately understanding that they were demons. Specifically, biblical demons, not the generic ones that are churned out in every fantasy setting. And they inspire more fear. It's much scarier to face the Lord of the Pit from Heroes 3 than any demon from Heroes 5.
However, the generally accepted sign of "demonicity" is probably the presence of fire and horns, rather than some vague criteria for matching the Bible or other games. In this sense, the demons from the 6th part became less canonical, although I wouldn't say that they lost much because of it. But that's just my opinion.
Bow down and hear our cry,
Our earthly rulers falter,
Our people drift and die,
The walls of gold entomb us,
The swords of scorn divide,
Take not thy thunder from us,
Take away our pride.
G.K. Chesterton: English Hymnal