Only further data can determine whether this is a general feature of some particular Dhofari dialect (perhaps the second language dialect of Arabic spoken by Shihri speakers?) or just an unusual feature of El-Kathiri's idiolect. However, if this construction was not simply idiolectal, its origins seem more likely to lie in Jibbali than in Dhofari Arabic, since no parallels have been found in any Arabic dialect of the Arabian Peninsula.A forthcoming article I recently came across, Pronominalization and Clitic Doubling in Syrian and Omani Arabic, changes the picture for this region. In a paper primarily focused on the generative syntax of clitic doubling rather than on its history, Peter Hallman and Rashid Al-Balushi demonstrate for the first time that the Arabic variety of al-Batinah in the north of Oman has productive clitic doubling, and that its distribution (definite/specific DO/IO/PrepO/Poss, no marker) largely matches El-Kathiri's usage a century earlier. Clitic doubling of this type thus a widespread Omani feature, not a Dhofar-specific one, and certainly not a merely idiolectal one.
Note that the dialect of Al-Batinah, like that of Dhofar, is a dialect with q for historic qāf, representing the earliest stratum of Arabic to reach the region. One hypothesis could be that clitic doubling of this type is a Modern South Arabian (MSA) substratum feature, calqued into the first Arabic varieties to reach Oman but never reaching the g-dialects that first come to mind when one thinks of Arabian dialects. On the other hand, no further evidence has yet come to light for clitic doubling in MSA; based purely on the available data, it seems equally or more plausible that this type of clitic doubling arose spontaneously in Omani Arabic and was calqued into Jibbali by bilinguals such as El-Kathiri. Much more dialectological data is needed to decide the question; available descriptions are evidently far from complete. In either case, independent origin appears far likelier than any kind of historic connection with the rather different types of clitic doubling observed in other parts of the Arabic-speaking world.