Bonding in Zeise's salt
The bond between $\ce {Pt} $ and ethene is not purely a $\sigma $ bond and also not a pure $\pi $ bond. The bonding  actually consists of a combination of both bonding and back-bonding effect. 


If you look into the Molecular Orbital Diagram of Ethene, the picture will be more clear. For the formation of bond between the metal and the ligand, electrons from filled $\pi $-bonding MO of ethene ($\pi_b $) is donated to the vacant orbitals of Platinum. And electrons from the filled orbitals of $\ce {Pt} $ is back-donated to the vacant $\pi^*$ orbitals of ethene. Thus the bonding would have been a $\sigma $ bond if the electrons are donated from a $\sigma_b $  or $\sigma_{nb} $ orbitals. But here the bonding mainly is $\pi $ donation and $\pi$ acceptance ( known as Synergic effect).


Thus, it would be better not to consider the bond as $\sigma $ bond, but may be considered more of a $\pi $ type but also not a pure one due to the back-bonding.