There's nothing about Sephiroth's 'resurrection' that's' wholly inconsistent with the game. Kadaj, Yazoo and Loz are manifested fragments of Sephiroth's spirit. We know, from the game, that the spirit of someone powerful yet dead can take on physical form and interact directly with the world like a normal person - recall the 'Spirit Bodies' of the Cetra who guard the Temple of the Ancients.
To make Sephiroth 'come back' in the film, Kadaj absorbs a quantity of Jenova's cells. Reuniting body and soul, in other words. Sephiroth's fully capable of inhabiting a body comprised solely of Jenova's cells, as shown in the game when he uses Jenova's headless body as a surrogate.

Sephiroth's death at the end of the game is easily reconciled with what's in the film: defeated, he died as his spirit was washed away into the Lifestream. Jenova's tainted spirit energy experienced the same, eventually being spread across the world to cause Geostigma in anyone it touched, or anyone carrying her cells already. Over time, the shattered remains of Sephiroth's spirit were able to crawl back out of the Lifestream, as the incomplete trio of beings we know from the film.