Is Ruki sound law a Satem variant of "Rhotacism"
English PIE Russian
ear h₂ṓws ухо /úxo/
sear *sh₂ews- сухо /súxo/
deer *dʰéws дух /dux/
alder h₂élis- ольха /olʹxá/
their ??? тех /tex/
No. Some instances of Proto-Indo-European *s were rhotacized in Germanic; some instances of PIE *s went to /x/ in Slavic by the Ruki rule. There is some overlap between the two sets, but the environments of the changes are different and they do not share any phonetic motivation, so it's meaningless to call one change a "variant" of the other. In Greek, most PIE *s went to /h/, but that doesn't make debuccalization a variant of the Ruki rule.
No. The Russian 'х' /x/ does not count as a rhotic sound despite the fact that some French r's are pronounced now in a very similar way. The Russian /x/ is the end product of a longer chain of sound shifts /s/ -> /ʂ/ -> /x/ in the RUKI environment.
High German shows a similar sound shift, the group /rs/ became /rʃ/ (written rsch) as exemplified by words like Kirsche "cherry", Arsch "arse", or Bursche "bloke, guy". However, this sound shift occurred much later and independently from the action of the RUKI law and affected only German proper, even Dutch is not affected by this (except for a small part of Limburgish, when you subsume it under the Dutch dachsprache).