Maybe a stupid question but what other large vessels have such a torpedo protection system?
This type of TDS was commonplace on WW2-era warships, usually on heavy cruisers (~10,000 tons) and larger. For example, this is an Iowa-class battleship's armor scheme - you can see the similarities in layout, minus the armor belt which does not exist in non-battleships.
I don't think any other modern warship has a similar layout except for large aircraft carriers, because modern naval doctrine treats surface combatants like glass cannons. No armor, no TDS, or any other on-board damage mitigation methods. Only SAMs and CIWS for defense.
It is possible that the Soviets constructed the Kirovs with this type of TDS considering their size, but unlikely. Even the 16,000-ton Zumwalts was constructed with no TDS, as you can see. Only possibility of this TDS on modern warships is perhaps LHDs like the Wasp-class.
Note that the Zumwalt does seem to have a double bottom, even if it has no TDS on the belt.