So there are a few class features in Tasha's that have a duration that involves concentration. For instance, Ranger's Favored Foe:

"When you hit a creature with an attack roll, you can call on your mystical bond with nature to mark the target as your favored enemy for 1 minute or until you lose your concentration (as if you were concentrating on a spell)."

Concentration is usually a pretty standard "you only get to concentrate on one thing" rule in 5E, but there's a bit of a loophole in RAW here. Here's what concentration has to say about how it ends in regards to starting something else that requires concentration:

"Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once."

Favored Foe is not a spell. It does not require you to have no other concentration spell cast in order to activate it. The language of both leads me to believe that you could cast a concentration spell (such as Hunter's Mark) and then use Favored Foe. Concentration does not end when you concentrate on something else: it ends "if you cast another spell that requires concentration" and Favored Foe is not a spell. Notably, this does not work the other way around -- you can't use Favored Foe and then cast Hunter's Mark, since Favored Foe ends when you cast a concentration spell.

Is there something additional I'm missing? Or is this just a strange loophole now that there exist concentration abilities that are not spells?

As far as I know, the answer is no. You cannot use favored foe and concentrate on a spell at the same time. This is why most people think the feature is useless. 

I think the part “as if concentrating on a spell” means exactly that — you treat concentrating on that particular feature as if you were concentrating on a spell, even if it isn’t one. From there, all the rules and requirements that go along with concentrating on a spell then are transferred to that feature.

RAI is concentration is used as a balancing mechanic so you can't combine certain effects easily. For example, Trickery Domain Cleric's "Invoke Duplicity" is a powerful feature for spellcasting. It can let you increase the range of spells, use touch spells without any risk, and so on. You can place it anywhere within range, even in the air, and it can pass through objects and obstacles etc. For 2nd level it's a powerful feature with a lot of tactical advantages and, of course, can potentially confuse enemies, provide distractions, lure enemies away or into traps, etc. This duplicate cannot be destroyed or dispelled. It isn't described as magical either so it is immune to the effects of Antimagic Fields. If it wasn't for concentration there'd be no way to counter this powerful tactical ability you have. Now imagine this combined with concentration spells - the combos you could pull off would be insanely OP.

Concentration serves to curb that OPness. It levels thing out. There are ways around concentration but they require a lot in other resources like magic items, time, gold, preparation or such as.

So, basically, if a feature says it requires concentration as if concentrating on a spell then you treat that feature like a concentration spell for the purposes of the concentration rules.

Just found the official source - in the 10 things to remember section of TCoE;

7. Concentration

As soon as you start casting a spell or using a special ability that requires concentration, your concentration on another effect ends instantly