Non-magical light is light from a non-magical source: torches, lanterns, a bonfire, lava, the sun (assuming a physics basis for the sun in your world) etc. None of these penetrate the darkness.
Magical light is light from a magical source: spells, class powers that are magical in nature, magic items etc. The corollary of non-magical light not illuminating the darkness is that magical light does.
The fact that the darkness dispels spells of 2nd level or lower is a furphy - yes such spells are dispelled but higher level spells are not and neither are sources of non-magical light that are not spells.
A magic item that emits light as a non-spell effect is not a spell so it is not dispelled or affected in any way by the darkness. As a source of magical light it will illuminate the darkness. Of course, for magic items that allow you to cast a spell, that spell may be affected depending on its level - a spell is a spell whether innate to a class or from a magic item.