I'm not even sure it's mathematically appropriate to talk about IQ differences as there's no proof IQ is a linear metric. IQ is defined to have a normal distribution, unlike most things which are measured to have a normal distribution.

With IQ tests, the only thing you know that if 2 people fill it out and one of them scores higher, they have a higher IQ. Based on this you can sort people into a list by increasing IQ, but the standard distribution is implied not discovered.

This is like having a double-sided scale and a bunch of weights - you can similarly compare the weights to each other, and sometimes the arm of the scale will lean to the left, sometimes to the right, by a little or lot - you can postulate that the weights are normally distributed are normally distributed, but they are absolutely not required to be (I can choose them any way I like), so your assumption would be wrong. We know this because we have a direct, not just a comparative measure for weight.

I could make up an imaginary 'weight point' scale based on these comparisons, and say weights A is 5 WP heavier than B and C is also 5 WP heavier than A.

But A might be 100g, B might be 1g, and C might be 1kg.

This is what I think of when I see studies clamining the difference between 2 groups was 5 IQ points.