I see nothing there that implies it is a barrier to vision, just an active and utter absence of illumination.
You are quite right - there is nothing in the spell that says it blocks vision, just that the area is in Darkness.
However, a strict reading of normal darkness means you can't see through that (PHB p.183):
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a
subterranean vault, or in an area of magical darkness.
And a Heavily Obscured area is (PHB p.183):
A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see appendix A).
Which has been erratad as:
A heavily obscured area doesn’t blind you, but you are effectively blinded when you try to see something obscured by it.
So, darkness (magical or otherwise) creates a heavily obscured area. A heavily obscured area "blocks vision entirely".
Now, while it is clear what this means for "opaque fog, or dense foliage" is simple and straightforward - you can't see into this stuff and you can't see through it to stuff on the other side of it.
Applying this to darkness, however, seems to result in nonsense because, in the real world, darkness isn't a thing. In the real world darkness is the absence of light hitting your eyes from a certain direction. This can be because of an actual absence of light (underground) or because, even though the region is full of light none of it is coming your way (space). But this isn't the real world, is it?
So you have 3 options:
- Darkness works just like it says in the book - you cannot see into it or through it. This would be really cool for a gothic horror campaign even though it would make navigating at night ridiculously hard.
- Darkness (magical or not) works as it does in the real world - you can't see into it but you can see through it to illuminated areas beyond. I think this is what the rules intended even though they and the errata were poorly drafted.
- Normal darkness works like 2. Magical darkness works like 1. There is no support for this in the Darkness spell description but this is how it worked in prior editions.
Its your world - make it fun.
There is no rule. It's up to your DM.
Don't mistake the game's rules (or lack thereof) for laws of physics in the D&D universe.
There are a lot of areas where the rules don't get specific about every detail of how something works because it's not, generally speaking, important. This is one of those areas.
For the purpose of using alchemist's fire in a fight, it burns for some indefinite amount of time that exceeds the length of the fight. Even two minutes is usually much longer than any fight lasts, so 'until extinguished' is sufficient definition for that purpose.
Similarly, presumably the flame produces some amount of light, but how much isn't specified, so it's left up to the DM to decide. That doesn't mean it produces no light. It just means it's not specified.
Best Answer
A distinction exists
In the rules on damage resistance, the following example is given:
First of all, this example gives evidence that "resistance to all nonmagical damage" is a valid type of damage resistance, and that the phrase "nonmagical damage" is itself a distinct category of damage (presumably defined as "damage that is not magical"). Additionally, because the example is being used to demonstrate that multiple applicable resistances do not stack, we can conclude that "resistance to all nonmagical damage" would grant resistance to damage caused by a nonmagical fire. If it granted resistance to damage caused by a magical fire as well, then the example wouldn't need to specify that the fire in question was nonmagical, thus I assert that "damage caused by a nonmagical fire" can be called "nonmagical fire damage" and "damage caused by a magical fire" can be called "magical fire damage".
Is "magical" a damage type?
"Magical" is not a damage type. The rules on damage types are short, in fact they mostly say "Damage types have no rules of their own", but they include a list of all the damage types and "magical" is not one of them. If you look through all the books you will not find an effect which simply "deals magical damage". It never exists in isolation because it is not a damage type.
What is "magical damage" if it is not a damage type?
"Magical" is a modifier that can be applied to damage, just like it can be applied to almost anything else. Fire created by magic is "magical flames". Darkness created by magic is "magical darkness". In the same way, damage caused by magic is "magical damage" even though "magical" is not a damage type and the damage also has a type that isn't "magical".
As an example lets take a +1 longsword. Nonmagical longswords deal slashing damage. Magical longswords also deal slashing damage. However, Nonmagical longswords deal nonmagical slashing damage while magical longswords deal magical slashing damage. Thus, a +1 longsword deals magical damage.
Maybe the example in the Damage Resistance rules is a mistake?
Although I can find no references directly to "magical damage", there are several cases of resistance to "nonmagical damage" or a subset of it, and which do not use the "damage from nonmagical attacks" phrasing. From things listed in the Basic rules, the spell gaseous form grants "resistance to nonmagical damage", the spell stoneskin grants "resistance to nonmagical bludgeoning, piercing, and slashing damage", and the magic item armor of invulnerability grants "resistance to nonmagical damage". Looking outside the Basic Rules, Demon Lords from Mordenkainen's Tome of Foes, such as the Demogorgon on page 144, have Damage Immunity to "bludgeoning, piercing, and slashing that is nonmagical." I find it unlikely that all of these are mistakes.
Maybe it means something else?
The most authoritative source available for how to determine whether an effect is magical comes from the question "Is the breath weapon of a dragon magical?" answered in the Sage Advice Compendium. There is a lot of information there, but the most relevant part is this sentence:
Thus armor of invulnerability is used as the canonical example for "protecting you from damage caused by a nonmagical effect". I'm not sure how much clearer it could be.
In conclusion
The phrase "nonmagical damage" is officially used in multiple places to mean "damage caused by an effect/feature/item that is not magical", using the typical definition of "magical". To complement that, the phrase "magical damage" would sensibly mean "damage caused by an effect/feature/item that is magical", though I haven't found that phrase used anywhere. Thus it is sensible to talk about "resistance to nonmagical damage", and "ways to cause nonmagical damage".