I made a quick Sketchfab account and uploaded this tiled sphere as an obj via Tool> Export from ZB2020.1.4 without apparent issue:
Likewise, there were no problems importing it into any other program I tried.
I can only suggest there may be something problematic with your geometry or UVs. It might also be useful to describe how you are exporting your model.
Otherwise this is an issue with your target application, and any questions or issues regarding its use should be directed towards Sketchfab support resources or other Sketchfab users.
If you’d like to bypass the need for tiling altogether, you can convert the applied tiled texture into polypaint in ZBrush. Remember that polypaint detail depends on mesh resolution, so your mesh will need to be subdivided sufficiently to capture all the tiled detail. Topological quality concerns also apply, so if your polygons are non-square it may lead to suboptimal results.
Once converted to polypaint, you can create a new texture based on that polypaint without the need for any tiling. If exported and imported correctly, any program that can display a UV texture map should then be able to display your desired results without the need for any tiling.