When I think about such structure, I draw all valence electrons around the atoms and connect them somehow reasonably. There are two ways to connect the hydrogens to xenon. Either directly bonded as H-Xe bonds, which for me does not feel right here, or as part of OH groups, which also make more sense in the "acid" part.
By connecting everything that way, you end up with:
This let you end up with a lone pair at xenon which is the reason for the non-tetrahedral structure.
A quick and dirty quantum calculation shows what I mean. By calculating the ELF (Electron Localization Function), you can easily see where the electrons are located. The lone pair is shown by the yellow volume surrounding no atom.
This structure is not clear from the Lewis formula shown on Wikipedia, but can be seen in the ball and stick representation that is shown there (don't care about the "flipped" hydrogens):
 ORCA 4.1.2, best functional of the planet B3LYP def2-QZVP // Crest 2.6, Visualization with Chimera, iso value 0.8 ... whatever ... camels? ... what unit has the ELF?