Short Answer:
I think, in this case, the answer is very simple: Rukmī's (goddess Rukmiṇī's brother), murder at the hands of Lord Balarāma wasn't justified, at least not from vyāvahārika level perspectives.
Discussion:
First, let's re-visit the incident. All story remain same as cited (from the Śrila Prabhupada's version of Bhāgvatam) in the question itself.
However, in the 'dvaitavada' acharya Vijay-dhvaja's (VJ) commentary version (called 'Pada-Ratnāvalī') of Bhāgvatam, there's another verse added to verse ŚB 10.61.32 as an addendum as follows:
Agitated with anger like the swelling ocean under the full moon, the glorious Balarama whose eyes were naturally reddish, became fiery
with extreme rage and he staked a wager of ten crores (of gold coins).
As per rules of that game, Balarama rightly won that bet. But Rukmi resorted to false pretext and said, "I have won the bet. Let the
umpires declare their decision".
32-A. VJ's Text : “So be it” said Dantavakra of Kalinga showing his teeth (grinning) at Balarāma. Balarāma boiled with rage but (controlled himself and) observed silence.
Taken from Motilal Banarsidass's rendtion of Śrīmad-Bhāgavatam
As we see, by verse 31, Balarāma is already at anger-maxima. Add to that in 32.a - the so called "judge - Dantavakra" also indulge in thuggery and mockery, and by ŚB 10.61.36 , Rukmī had crossed 'the line', even neglecting the words of ākāshvāṇī much before in ŚB 10.61.33.
Now, it's well-known that anger (krodha) is one of the ṣaḍaripu (षडरिपु), and as such is very difficult to control, for the demigods too, and sometimes even for the gods also, even if done as a past-time (līlā). Like: god Śiva beheading Vināyaka
Further, Balarāma, is none other than a manifestation of Ādi Śeṣa / Sāṅkarṣaṇa - the vyuha of Vishnu in the mode of tamas and thus anger (pralaya kālāgni being the source of it) comes naturally to Balarāma.
And being born as a Human, in Kshatirya varṇa, Rajo-guna (action) will naturally find abundance in him (Manusmṛiti 12.46), and that when coupled with anger (tamas), will sometimes manifest in 'action (Rajas) - brawl' and thus 'an apparently adharmika action' - like unduly killing someone (Tamas).
Thus,
Whatever Balarāma did was out of pure rage and anger against the thuggery happening at the dice game. Notwithstanding that, perhaps it wasn't so much dhārmika on Balarām's part to kill/hurt Rukmī and his demon-pals.
Even Bhagvān Śrī Kṛṣṇa kept his silence on this [ŚB 10.61.39], lest he should invite rebuke either from his spouse - Rukmiṇī', who has just lost her brother over a petulant brawl, or from Lord Balarāma, who felt right in his decision to murder the dice game's opponent on account of unfair play.
In any case, the silence from svayam Bhagvān himself, says he neither favored the act of murder nor opposed it unequivocally. Thus, Rukmī's killing by Balarama cannot be adjudicated as 'unequivocally justified'.
On a side note, one can also argue that since the 'judge of the game' was also involved in thuggery, and everyone conveniently ignored the celestial admittance of Balarāma's victory - creating ample amount of adharma, thus, Balarāma was right in bringing everyone to justice, as BG 4.7 & 4.8 holds good, and he himself being an 'avatāra', thus, killing was justified.
But, more importantly - I'd say, what is there to justify or not, if - How do we solve the contradiction of Rukmi being alive during the war, though Balarama had killed him before? this is true?!
