What gas has the highest refractive index?
The question has to be more specific to get a specific answer. 

Even in the table linked in the OP, bromine gas (1.001132) has a higher index of refraction than 1.000773.  

At zero degrees C, 5462 Angstroms, and atmospheric pressure, The Refractive Index Dispersion and Polarization of Gases (1936) reports:


  $\ce{Si2H6}$ 1.0016574 


$\ce{Si2H6}$ , disilane, is a gas at room temperature and atmospheric pressure.  

The index of refraction is extremely dependent upon pressure.  

As an introduction, see INDEX OF REFRACTION AND DISPERSION OF SEVERAL GASES IN CERENKOV COUNTER USE where indexes of refraction of gases as high as 1.02963 (for 182.79 psig ethane) are measured.