nerdist.com and the tactical tag blog, this blaster has a capacity of 24 rounds, which means 6 per each of the 4 cylinders. Redditor lSherlockl pointed out that each turret looks like it holds at least 8 rounds - which, at a glance, it does - for a total of 32.
If the Doominator holds 8 rounds per turret, we should expect the spacing between the upper and lower pairs of darts in the picture to be a little less than sin(45 deg) = 0.707 times the spacing between the middle two darts. (It's a little less because of parallax.) If there are 6 darts in each cylinder we should expect the spacing between the upper and lower pairs of darts to be a little less than sin(30 deg) = 0.5 times the spacing between the middle two darts.
I've measured the spacing of each set of adjacent darts on the cylinder which is the closest to the camera. Each measurement was taken between the tops of the darts where possible, and otherwise from the bottoms of each dart. All measurements are accurate to +- 1 pixel due to the slight blurring of the edges of the darts.
- Highest to higher middle: 51 pixels
- Middle two: 111 pixels
- Lower middle to lowest: 54 pixels
If we assume that the turrets are rotated such that there is a single dart at the top of the cylinder, then, of course, this would mean that each cylinder holds only 6 darts. This is a plausible assumption; zooming in on the visible part of the back of the uppermost plunger tube reveals what appears to be one dart's worth of air holes, not two.
This image might not be representative of the final design of this blaster. Note the lack of a connection between the upper part of the active cylinder and the body of the blaster where the plunger tube presumably lies. Either the PT leaps forwards during firing or some parts are missing in this picture.
Overall, if I had to call this one, I'd say that each cylinder will hold 6 darts. This is rather disappointing, given that this blaster is a potential (inferior) substitute for the now hard to find Rampage and EAT. The need to switch cylinders every 6 (or 8) shots is enough of an annoyance, not to mention the effective decrease in capacity that results from switching before a cylinder is completely depleted. If this blaster holds 24 rounds, while Rampages come with a 25-round drums, then this fact is just the disappointing icing on the disappointment cake.
Edit: I was unaware of this picture, commented on by Blasterlabs here, which shows the Doominator's top cylinder from an angle which makes the fact that it is hexagonal clear. (Well, this is a little embarrassing.) Credit goes to redditor ironmagnus and the anonymous commenter below for pointing this out to me.
Second edit: Now, it's official. Hasbro has announced that this blaster holds 24 darts.