In the formation of [Ni(CO)4], oxidation state of Ni is O and its electronic
configuration is [Ar]3d84s2.
Hence, we have
In [Ni(CN)4]2−, Ni is in +2 oxidation state and CN− is a strong ligand and as it approaches the metal ion, the electrons must pair up.
In [NiCl4]2−,Cl− provides a weak field ligand. It is therefore, unable to pair up the unpaired electrons of the 3d orbitals.