Periophthalmus waltoni occurs in the area, but you would need to collect specimens to confirm the identification. I would recommend the following literature for further reading (Jaafar & Larson 2008 provide the most recent identification key):
Murdy, E. O. 1989. A taxonomic revision and cladistic analysis of the oxudercine gobies (Gobiidae: Oxudercinae). Records of the Australian Museum, Supplement 11: 1-93.
Jaafar, Z. and H. K. Larson 2008. A new species of mudskipper, Periophthalmus takita (Teleostei: Gobiidae: Oxydercinae), from Australia, with a key to the genus. Zoological Science 25: 946-952.
Ghanbarifardi, M., M. Aliabadian, H. R. Esmaeili and G. Polgar 2014. Morphological divergence in the Walton's mudskipper, Periophthalmus waltoni Koumans, 1941, from the Persian Gulf and Gulf of Oman (Gobioidei: Gobiidae). Zoology in the Middle East 60 (2): 133-143.