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Eraserman, you could well be right.

Eraserman,I think 'may' is a tricky word these days. In current English usage it is often used in the same way as 'might' - implying a degree of possibility.
"It may/might rain today."
It is also used interchangeably with 'can'.
"You may/can go to the ball."
Personally, I think in the preamble 'may' is used in the sense of 'can'.
(Although, interestingly, we are not being asked to show how we have linked the pairs - for instance, by listing them under the grid.)

My pairings go like this:
A pair involving contests by humans on foot.
A pair involving contests, but with humans sitting in/on a source of power.
A pair of ethnic groups.
A pair that both come under dictionary entries for the theme word - but in quite distinct difference from contest or ethnicity.

I think if people look under LAYER, rather than RELAY, things may slot into place a little better.

Betty2. None the wiser. Could you add a little more please?