I had a quick read of the journal article that press release is based on (not a medical researcher, but in another area of scientific research). Yes, they are talking about population-level effects, and most 37, 38, and 39 week babies will be indistinguishable from most 40 and 41 week ones – and given any two individual children, it could well be the 38 week one who is brighter/sportier/whatever than the 40 week one. The authors themselves talk about the results in the context of routine (not for any medical reason) induction being offered at 39 weeks (which is not something I think is generally considered in the UK anyway, but apparently can be in the US). So they aren't suggesting we need to worry about babies who naturally come at 37, 38, 39 weeks, or that guidance for offering induction due to medical need should change – it's more of a 'all else being equal, maybe if baby doesn't come on his/her own at 39 weeks, you should leave them cooking a little longer...'.
Even at the population level, the study lumps quite a lot together. They looked at the development of the children 7 times between 4 months and 3 years (using the same questionnaires most health visitors use here) and counting up any 'fail' in any category at any age. A child only has to be 'in the black' once at one age to count, even if they went on to be on track in that category in later checks. There's nothing in the main paper about how the rate of fails changes, or doesn't change with age, and to me that's very important – if early term babies are more likely to 'fail' at 4 months, but have similar rates at 3 years, that's quite a different story than if the rates remain different at 3 years. (I would guess they didn't report this because they don't have enough data to draw robust conclusions without lumping all the data together, but that's inference on my part, they don't say anything about it.)
They do also look at gestations of children who were actually deemed eligible for early intervention, but there the results are a lot less robust. They can confidently say the risks are higher for children born before 37 weeks (which is obviously not news). From 37-41 weeks, there's potentially a slightly correlation between later birth and less risk of needing extra support, but the statistics show it's not robust, i.e., it could just be a random sampling effect.
Sorry, that's quite an essay – I hope it's a helpful one.