Sorry, your understanding of electricity needs some help. DC means "direct current", and that means that the current always flows in one direction. A dry cell or a storage battery puts out direct current, and it always measures some steady value. AC means "alternating current", and here the current changes direction as time goes on. Power from the wall is AC, and it changes direction 60 times per second (60 cycle or 60 hertz). Bike dynos produce AC, with the current changing direction more often as you go faster. The term "alternator" is accurate for such a generator, but it usually applies specifically to the three-phase AC generators designed for cars and other vehicles. Both AC and DC require a closed circuit, i.e. two continuous current paths. Wire and bike frame are both capable of carrying AC or DC, and do not care which one they are carrying.

Dynamo lights containing LEDs are designed to run off of AC power, but the LED itself is energized by DC. LED battery lights don't contain a rectifier. A commercial dyno headlight will contain a device called a rectifier (the bridge, which can include the LEDs) to "straighten" the current flow from alternating to direct, or unidirectional. Based on efficiency and other functions, such as pulsation and having a standlight, there is also a filter (the capacitors) which smooths the pulsing unidirectional current the rectifier produces.

DC generators can and have been made, but are not common for bikes, if they have ever been used. They are basically an AC generator with a built-in mechanical rectifier called a commutator. The commutator requires slipping contacts called brushes. In Thomas Edison's day these actually looked like brushes, with the bristles being short copper wires. Today they are usually chunks of carbon. No matter what the material, a brush/commutator adds weight, cost, noise, sparks, electrical interference (often), and the need for servicing. Brushes wear and need replacement, and commutators need cleaning. They are really not suitable for long term reliability in the hands of users who do not know how or when to service electrical machines, which includes at least 99.9% of all cyclists.

But fundamentally the wiring arrangement is not an indicator of an AC or DC system, at least for small power systems like bike lighting.

I don't know what benefit your battery pack gave you, but it seems to have done no harm if the lights still worked. And as an electrical engineer that does not surprise me.