It is by design!
There are two tiers of items while leveling from 60-69, at 61 and 66.
Required Level 61 - These items are actually scaled to be appropriate for anywhere between level 61 and level 65. They just all have a chance at dropping as soon as you reach level 61. This is actually better than the old system.
To compare with vanilla Diablo 3, this would be like all gear from levels 51-56 saying "requires level 51" and having a chance of dropping as soon as you reach level 51. This gives you a better chance to find upgrades that will actually stick for a while instead of being replaced every level or two.
Required Level 66 - Same as above, but for levels 66-69.
The risk with this new system is that you could very well find lots of great gear scaled for level 65 at level 61, and go a long time without any upgrades.
I tried to paraphrase this so it was a little more understandable, but here's the explanation in the words of a blue poster over on the diablo forums:
It looks like there was a little confusion on this topic, so allow me to clarify - There is not a bug involved here. Required level is not the same thing
as an item’s power level, and it definitely does not mean a level 69
character should feel uncomfortable about using an item that specifies
“Requires Level 61.” Items saying "Requires Level 61" on them is by
design. The item can be at a power level intended for level 68 or 69
characters but we let players use it at Level 61 - this is
A primary boon of this approach is you know that items you find early
on in your leveling experience (around 61-62) aren't replaced
immediately upon reaching 63. That awesome item you found at 61 should
be able to stick with you up through 69. When there are too many tiers
of items, you transition through them rapidly and the items start to
feel transient. Why bother gemming or enchanting an item if you expect
to find an upgrade in 30 minutes? The Mystic’s Enchanting is powerful,
but it doesn't feel worth using if you don’t have confidence your item
will still be useful in 2 levels. Another benefit of this design
choice is that it is alt-friendly. We think it's really fun to have
the option to twink characters. Why not allow items you find at the
upper echelons of the 60's to be passed down to your new characters
This does have some downsides, including that upgrades can feel a
little sparse between the latter levels before cap (66-69). However,
in this situation, we felt the benefits outweighed the detriments and
it keeps the element of randomness that we feel is core to the Diablo
experience. We want to ensure there is a chance to find an amazing top
tier item the moment you ding 61 and get to hold on to it for hours if
fortune smiles upon you, though that may mean it takes a little longer
to find an upgrade for that particular slot.