Yes. This still requires concentration
DMG p. 141
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. Certain items make
exceptions to these rules, changing the casting time, duration, or
other parts of a spell.
The item specifically calls out the exception to the casting time of Conjure Elemental and specifically limits said cast to only summoning Air Elementals.
DMG p 158
While incense is burning in this censer, you can use an action to
speak the censer's command word and summon an air elemental, as if you
had cast the conjure elemental spell.
The seeming confusion appears to be in the definition of the idiom "as if".
I think that interpretation of the first definition by some like @Carcosa and @NautArch here seems to be the contention.
1: as it would be if
So in the case of this item you speak a command word instead of doing the full casting of the spell. So maybe you did cast the spell or maybe the item cast the spell but since the description of the item doesn't say that you don't have to maintain concentration you do. There is no specific exception to the rules presented on page 141.
This means that you can simply replace "as if" as follows:
[...] you can use an action to speak the censer's command word and summon an air elemental, as it would be if you had cast the conjure elemental spell.
Thus treat the spell as though you had cast it therefore all rules apply normally except where specifically told to ignore them.
Take for example:
Blackrazor DMG p217
Blackrazor can cast the haste spell on you once per day. It decides
when to cast the spell and maintains concentration on it so that you
don't have to.
Potion of Speed DMG p188
When you drink this potion, you gain the effect of the haste spell for
1 minute (no concentration required).
Potion of Heroism DMG p188
For the same duration, you are under the effect of the bless spell (no
For brevity Potion of Diminution, Potion of Growth, Potion of Gaseous Form also have the same override to p141.