A bunch of random thoughts:
Comparing pixel counts of ship and the gun, turret with the barrel seems to be little under 19 meters long.
Visible barrel is some 9 meters long, while turret is some 10 meters long. Thinner part of the barrel seem to be 0.9 meters in diameter. Though, of course, at this point room for measurement error is quite big, so it's really +/- a decimeter or two.
Using the images of the big US NavSea and BAE gun - their barrel is some 60 cm wide vertically (horizontally it's slimmer, around 35-40 cm). The hole in the barrel for the projectile is some 12-ish cm wide.
IF the underlying concept and technology is similar, which it may not be, then we might be looking at a larger caliber weapon, possibly by up to 50%. (12 cm hole may not equal to projectile caliber! it may very well be less)
If the concept is different, and chinese gun is really a coil gun with a round barrel - then who knows what the caliber is. It could be more or less.
But it does seem the gun itself is scaled for operational sized projectiles. the BAE had some future rounds on display and a 127/155mm rounds had an extra 80-100 percent of sabot width around them.
IF we're looking at 120mm for BAE gun and 180mm for Chinese gun, overall projectile diameter then may be 90-100mm. (for similar tech and concept). If a coilgun approach and different engineering yields different barrel thickness/round diameter ratios, it may be more. or less. Of course, apple to apple comparisons between diameter of conventional 155mm round and railgun round that fits in 155mm barrel are not applicable.
The way I see it, the development of Chinese gun itself should be finished. The development cycle usually calls for lab tests to see what techonology is ready for. Then some prototypes are made. Then the armed forces give some more precise requirements and new prototypes are made, usually scaled up. Then the whole thing, if the re-engineering process holds up, is thoroughly tested, in a lab. Then somplace outside. Usually there is more reengineering needed. Basically, before putting a gun to sea, and especially before a whole turret is engineered around it, the gun itself is ready. Can't see they'd use a developmental tech and take it out to sea to test it. So 055 batch 2 does seem VERY possible as actual application. Not only that, but i'd expect the turret design to be pretty definite as well. With barrel design being almost surely very definite.
As for guidance- of course it's going to feature guided rounds. Two lines of reasoning: One says that if you're going to shoot something out to 200+ km, you NEED guidance. The gun would be useless without it. The other says that acceleration of the round is made gradually over the length of the barrel. So mach 6 over 9-11 meters. Compared to acceleration of a regular gun where majority of acceleration happens within decimeters.
Some said it could be electrochemical gun. Such guns have quite normal looking barrels, as far as i could see. They're basically still regular guns with propellant, only the ignition of the propellant is done differently (and different kind of chemical propellants are used). Thus the barrel itself is pretty much the same as in any gun. Thus it is usually quite long and thin. As opposed to this barrel here that we see.
Finally - could reveals like these cause an arms race? Not in themselves, no. But having several high profile weapons that seem to match US tech level or exceed it be revealed within a decade may cause an arms race. J20, Hypersonic glide warhead, Railgun, future H20 bomber - all those revealed within a decade may cause a media frenzy which may influence the policy makers to succumb to US DoD appetites and actually give US DoD big increases in funding. Some of it may be for new tech, but some of it may be for more of existing weapons. Just as Soviet Union at times went for the numbers when it didn't have the technology ready. And then we get a vicious circle of both sides arming more and more due to perceived edge of the other side. I do fear we may be at the brink of a new arms race, one to unravel during 2020s.