ᴺS. [N.] ^rui n. “hunt, hunting, *chase” (Category: to Hunt)
A noun appearing as N. rhui(w) “hunt, hunting” in The Etymologies of the 1930s derived from the root ᴹ√ROY¹ “chase”, cognate to ᴹQ. roime (Ety/ROY¹). Here the initial r became voiceless rh as was usual in Noldorin, while it seems the medial m became w and then vanished.
Conceptual Development: The Gnomish Lexicon of the 1910s had similarly formed G. raust “hunt, chase”, clearly based on the early root ᴱ√RAVA that was the bases for “hunt” words in the contemporaneous Qenya Lexicon, as suggested by Christopher Tolkien (GL/65; QL/79; LT1A/Meássë).
Neo-Sindarin: Since the unvoicing of initial liquids did not occur in Sindarin, many people adapt this word as ᴺS. rui for purposes of Neo-Sindarin, as suggested in Hiswelókë’s Sindarin Dictionary (HSD). I would extend its meaning to “hunt, hunting, *chase”, to make it more distinct from “hunting” words based on [N.] fara-.
Reference ✧ Ety/ROY¹ ✧ “hunt, hunting”
|ᴹ√ROY¹ > rhui(w)||[rojme] > [roime] > [ruime] > [ruim] > [r̥uim] > [r̥uiv] > [r̥ui]||✧ Ety/ROY¹|
References ✧ GL/65; LT1A/Meássë
|ᴱ√RAVA > raust||[raβste] > [ravste] > [ravst] > [raust]||✧ LT1A/Meássë|