The Pakistani Babur is a case where a country with access to mini-turbojet (China), used a large Tomahawk based airframe to supply a large amount of fuel. They managed 700-800km IIRC.
That would fit the claimed 700km of the Soumar.
As the Hoveizieh is visible at the exhibition, it seems to have a Toloue based engine. It has no exotic afterburner and is just on a spacey nacelle with a somewhat deep inlet duct resulting in that long nacelle.
I have the feeling the Iranian 700km turbojet variant of the Kh-55 was shown for this open exhibition while the range figure of 1350km is in fact for variant with a Kh-55 like turbofan that can't be shown at a open exhibition.
The turbofan claim and 1350km range figure would fit a reverse engineered Kh-55 variant that just runs for ~1,5 hours before failing while the original 80's vintage Soviet engine (a technological marvel) survives for more than 3 hours to reach the max. range. The less fuel necessary for a 1,5 hour engine operation could then be used for a larger warhead.
It seems certain that a turbojet based CM of that dimensions could never reach 1350km, even with the best airframe materials.
The whole project is probably still in high classified condition of critical weapon systems.
Despite no cruise flight footage was shown I belief their claim that the first turbojet variant did 700km and now they have managed to reverse engineer a Kh-55 turbofan with half the operating lifetime (at a economic price).
We have also to notice that the Ya Ali CM with its Toloue turbojet also had a range claim of 700km.