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Oxygen has less negative electron gain enthalpy than sulphur.

This statement is given in my book with a short reason:

due to compact size of oxygen

I'm unable to understand why. I would appreciate any worthy explanation for this.

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It is because Oxygen is first element of Oxygen family in its table and Electron gain enthaply decreasing from top to bottom in the group.

This exemption happens because of the reduced 2p orbital of Oxygen, there is enormous interelectronic r between the electrons in 2p orbitals thus Oxygen has less proclivity for an additional electron and the EGE of Oxygen is more positive than Sulphur.

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