It seems the translation is very correct, no one has given any good refutation of Skanda Purana's translation. I am no expert, bit have been able to understand what some of the original Sanskrit words meant.
The Sanskrit words for the statement that she was eight years old are like this, meaningsEnglishmeanings in brackets are mine:
Sa(she)kala(time)prayaya(course)aad(?)ashtavarsha (eight years).
Sanskrit source is here, check page number 182 (the Devanagari is labelled 902 in Nepali variant): http://vedicreserve.mum.edu/puranas/skanda_purana/skanda_purana_05avanti_03reva.pdf
Please note that the previous statement was about her birth and her being named Rukmini, so even if its referring to passage of eight years, the translation is basically correct: Yat Survantilkojanmanasahbharat. Tat sa Rukmininambrahmine kirttatada.
The English translation seems correct or close, and the Part 15 of the translation by Sanskrot scholars G.P. Bhatt, Jagdish Lal Shastri, Ganesh Vasudeo Tagare too mentions it as such.
The translation of Harivamsa used here claiming Rukmini was 16 during marriage is incorrect.
There is no Sanksrit word for sixteen mentioned in the transliteration: "shyAmAvadAtA sA hyAsItpR^ithuchArvAyatekShaNA". See here for comparison of Sanksrit words for sixteen:
http://spokensanskrit.org/index.php?mode=3&script=hk&tran_input=sixteen&direct=au
The Bhagwata Purana is based on mere belief that a mature age was the age of marriage for Hindu girls.
That is false as Manusmriti says even little girls can be married. The Puranas cited here were all written after Manusmriti.
Of course it is not impossible that there may be various versions about her age.
