Many items, such as potions, bypass the casting of the spell and confer the spell's effects, with their usual duration.
Rules as written, a potion requires concentration. See page 141 of the DMG:
In other words, you'd be stuck concentrating.
I disagree with your interpretation. The duration of a spell is not the same as the effect of the spell. You are not turned into the caster of the spell (for whom concentration would apply).
Now, if you wanted to argue that the text could be interpreted to say that, as was humorously suggested, the caster (wherever they might be) must concentrate on the spell, then you would have a reasonable argument, although it would lead to what seems to be a clearly erroneous conclusion.
And remember, all of the example potions that confer the effects of a spell requiring concentration (with one exception) go out of their way to say that you don't have to concentrate.
(Also, contrast your quote with the immediately previous sentence in the DMG.)
The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
But since potions bypass the casting of the spell, concentration cannot apply, as it is something that the caster does, and these spells explicitly bypass being cast.
Here's how the text reads:
"Casting a Spell
When a character casts any spell the same basic rules are followed, regardless of the character's class or the spell's effects.
...
Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends." - PBR p. 79.
Concentration is an element of duration, which is organized as a subtopic under the broader heading of "Casting a Spell." You therefore refers to the caster not a recipient of any particular spell effect. I'm talking about the arrangement of the document and its logic, which is clear from just looking at that page and section.
Now, the DMG gives us:
"Some magic items allow a user to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration. Many items, such as potions, bypass the casting of a spell and confer the spell's effects, with their usual duration." - DMG p. 141
My argument entirely rests on the fact that the drinker of a potion is explicitly not the caster of the spell, and concentration can only apply to the caster of a spell. If they were going to make an exception to say that drinkers of potions need to concentrate as if they had cast the spell, they would have had to specifically call it out (which they did not) since the general rule is that concentration is solely for the caster, not the recipient of an effect.
I understand where you are coming from with regards to the duration line. Concentration is considered part of duration, so "normal duration" should include concentration. This is a real problem with the text's clarity. But in the case of potions, if their duration did include concentration, they wouldn't work at all, since there is no caster to concentrate on them. It doesn't say the drinker is treated as the caster--it says they receive the effects of the spell while bypassing casting it.
I would have thought the statement in the DMG, already quoted above (including by you), that "the user of the item must concentrate if the spell requires concentration" is a very specific calling out of the need for drinkers of potions to concentrate!But since potions bypass the casting of the spell, concentration cannot apply, as it is something that the caster does, and these spells explicitly bypass being cast.
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My argument entirely rests on the fact that the drinker of a potion is explicitly not the caster of the spell, and concentration can only apply to the caster of a spell. If they were going to make an exception to say that drinkers of potions need to concentrate as if they had cast the spell, they would have had to specifically call it out

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Rulebook featuring "high magic" options, including a host of new spells.