**It's speculatively possible.**

I've searched if the manufacturer has made such a claim. However, they aren't making any claims. The only explicit claims they make [is a press reprint][1] about the specifications: that it flies at 2.65 km/s at an altitude of 20 km. Your link includes verified range figures of 350, 450, then 1000 km.

Perhaps one could determine if it's likely to be a scramjet indirectly, by analyzing if this performance could have been reached by another type of engine. First checking **rockets**: 

* The first 2.65 km/s of delta-V goes towards acceleration. For a (very good) solid rocket motor at Isp~=265, that requires `Wi/Wf=e`, in other words, 63% of the missile's mass just to get it to speed. 70% or more if the motor is discarded.  
* The [Breguet equation][2] for range in sustained aerodynamic flight is `R = V * L/D * Isp * ln (Wi/Wf)`.
* At a roughly estimated L/D=3 and fuel weight fraction of 0.35, `R = 2650 * 3 * Isp * 0.43 ~= 3400 * Isp`, for range in meters.
* Solid rocket propellant would produce Isp in the 230-270 range, giving a range of 850 km. This is close enough to 1000 km if some speed is traded for range or L/D exceeds 3.


It's not easy to research a weapon that's still under a lot of secrecy. I had hoped that Russian-language articles would be closer to the source, as they usually are, but all are clearly the work of analysts not involved in the missile's development. 

[This is the best one I managed to find][4]. It confirms again that the missile uses a synthetic hydrocarbon fuel and *"a special ramjet engine, which is characterized by supersonic combustion"*.
[Another article][5] digs into listing every test, including launch footage, and attempting to estimate the missile's exact shape and dimensions from OSINT.

Mass-wise, it's not advertised, but considering it's smaller than [the missile it replaces][3], it can't be more than 3,000 kg full. That leaves a best-case weight of 900 kg after acceleration, which falls 10% short of 315 kg fuel, 300 kg warhead, 300 kg airframe and engine, 100 kg guidance ~= 1,000 kg best-case estimate. 

So, it's possible to achieve the specifications achieved in early tests without using a scramjet engine. A combination of rockets or air-augmented rockets could reach this velocity and range. For the later tests, the warhead would have to be removed or greatly reduced.

However, this missile is a successor of a long line of ramjet missiles. The manufacturer doesn't explicitly state they're using a scramjet, but a ramjet would be ineffective at this speed. Its shape clearly indicates an airbreathing engine inside. Scramjet engines have been studied and tested extensively, in various forms.


Changing the equations to reflect a rocket to get to half speed, then a **scramjet** for the rest brings different math:

* Accelerating to 1.3 km/s with a solid rocket requires 40% mass in fuel, or 45% with the motor.
* Assuming a [very conservative][6] 700s Isp for the main engine, the remaining 1.4 km/s will take `1-1/e^(1400/7000)=18%` mass in fuel.
* The Breguet equation, after removing 18% spent on acceleration, computes as `R = 2650 * 3 * 700 * ln(0.82/0.65) ~= 1,292,927`, i.e. ~1,290 km.
* To reach the target range of 1,500 km, fuel fraction has to be increased a bit. At 40% fuel, estimated range increases to 1,738 km. 
* For a second stage at 1650 kg total, possible weight breakdown computes as 660 kg (40%) fuel, 550 kg airframe+engine, 340 kg warhead, 100 kg guidance.

From the articles about the missile, it sounds more probable that it uses a [dual-mode ramjet][7], rather than a straight scramjet. Dual mode ramjets are a cross between ramjet and scramjet, able to operate in both subsonic and supersonic combustion modes. This would allow an earlier takeover from booster to primary engine, improving range and payload capacity. It would also be more consistent with evolutionary development of the ramjet series and modest statements about a "special ramjet", rather than an entirely different engine.

With a **dual-mode ramjet**, the range estimate changes as follows: 
* Solid rocket booster is needed up to 700 m/s, consuming 26% mass in fuel, or 30% including the motor.
* At the same 700s Isp for the DMR, the remaining 2 km/s will take `1-1/e^(2000/7000)=25%` mass in fuel.
* Using another 15% for cruise, Breguet computes as `R = 2650 * 3 * 700 * ln(0.75/0.60) ~= 1,241 km`.
* This breaks down second stage weight at 2000 kg total, including 800 kg fuel, 600 kg airframe+engine, 400 kg warhead, 200 kg guidance.

That last version is consistent with current and intended range (presumably as the missile improves), appearance, and leaves margins for heavier components or lighter launch weight. 


**Summary**

* The missile's specifications are consistent with a scramjet engine.
* A dual-mode ramjet is also a possibility, consistent with the missile's history and pictures.
* Test results could be replicated with rockets, but it wouldn't leave enough room for a warhead.
* The engine appears to be a "live prototype" that's still being improved. It falls short of the theoretical abilities of a scramjet, and is more of an early iteration. 


  [1]: http://npomash.ru/press/ru/podrobnee240821.htm?l=0
  [2]: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node98.html
  [3]: https://en.wikipedia.org/wiki/P-800_Oniks
  [4]: https://reobzor.ru/news/2021/01/raketa-cirkon-rossijskaya-krylataya-giperzvukovaya-protivokorabelnaya-pkr-3m22-istoriya-sozdaniya-konstruktivnye-osobennosti-rezultaty-ispytanij
  [5]: https://militaryrussia-ru.translate.goog/blog/topic-718.html?_x_tr_sch=http&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
  [6]: https://www.sciencedirect.com/science/article/pii/S100093612100203X
  [7]: https://www.sto.nato.int/publications/STO%20Educational%20Notes/RTO-EN-AVT-150/EN-AVT-150-07.pdf