Quite possible, as the rig isn't seen again.
In contrast, Kruge's targeting rig is the very same that was seen in TMP. His small ship just has one such swiveling targeting chair in the background, while the TMP cruiser had two...
We see that Starfleet bridges are heavily "customized", perhaps according to the wishes of the skipper: certain workstations may be absent or present, differently situated, manned with differing numbers of personnel... Perhaps Klingons go for the same sort of customizing.
Another thing to consider: the BoP in ST3 probably isn't a new ship type at all. Kirk and Sulu seem intimately familiar with it, at least. It's possible that a few of the BoPs of the 2280s would have interior aesthetics that reflect the 2260s ones we saw on TOS cruisers, then. Kruge may have had a modern navigation bridge, but his secondary bridge or spy center or whatnot may have had the classic "blue plywood walls" style because refitting it was not such a priority.
Alternately, navigation bridges don't have to change much with times, since the ST4 style is not only seen in TNG, but also centuries earlier in ENT. But Kruge's mission-specific command center may have had to feature the hottest hot in new technology, and that would be blue plywood. The TOS and TAS cruisers in turn would be all-hot from the inside, that is, all-blue-plywood.
By the time of TNG, this hottest hot would change a bit, adopting more subdued colors - or then simply accruing a crust of dirt and rust, something that the other parts of the ships had received much earlier. For all we know, the ST4 navigation bridge was originally very TOS-like, too, with bright colors on clear walls, but five decades of maintenance neglect and the bolting of new consoles and other gear had turned it into the "fleet standard" of grimy looks.
Timo Saloniemi