I don’t think you can make the “Alternative description” field required.
Usually to change the TinyMCE behaviour, you have to find the related setting in the TinyMCE documentation (v5 is currently used by this MODX extra) and then either use an external config or change the system setting (if available).
In this case, the only related thing I could find is the option to disable the description.
Also, the extra “TinyMCE RTE” uses a custom plugin for images called “modximage”. It maybe would be possible to make the field required, but it certainly would require to change the plugin code.