Is it correct to assume that the Yiddish is exactly how the Gra wrote it in his own tongue (besides maybe a couple words of discrepancy here and there) or was it rewritten in Yiddish and is therefore not how he wrote it at first?
The third paragraph and second footnote in the introduction in the Hebrew version that you linked to (page 1 in the text, page 3 in the PDF) implies that we no longer have the original (probably-written-in-Yiddish) version. Thus, the Yiddish version you linked to would be a retranslation if the Hebrew.
(Also, the language1 of the Yiddish version you posted doesn't correspond to what I expect of a Lithuanian dialect of Yiddish, but I've never seen anything else written by the Gra in Yiddish, so I can't compare.)
1 The spelling is inconsistent, but it suggests a certain pronunciation. For example, it has נישט and ניש (="nish(t)") instead of the expected Lithuanian ניט (="nit"); it has דיא for "you", which suggests "di" instead of the expected Lithuanian "du"; it has פין (="fin") and קימט (="kimt") and װעסטי (="vesti") instead of the expected "fun" and "kumt" and "vestu", among others; it has both זײן and זאן for "to be", which suggests the pronunciation "zan" instead of the expected Lithuanian "zayn"; similarly, it has גלאך (="glakh") and דאן (="dan") instead of the expected "glaykh" and "dayn", among others; it has טאוט (="taut"!) instead of the expected "teyt". (We generally see a written "u", "ey", and "ay" pronounced as "i", "ay", and "a", but not the other way around, so the spellings here really do suggest the pronunciations.)
Additionally, it has דעס (="des") as an article, when Lithuanian Yiddish has no neuter gender.
All the evidence above points to Polish Yiddish as a likely dialect. I haven't mentioned the pointing of the text, as that could be reasonably assumed to be added, but it also points to a Polish pronunciation.