Yes, he is most likely including the primary laser in his assessment of firepower.
Here's the image referenced in the question that speaks to the 15,000 turbolasers that the Death Star carries.
According to the Star Wars Wiki, the empire operated over 25,000 Imperial Star Destroyers at it's height.
If you assume:
- The height of the Empire occurs around when the first Death Star is built (reasonable)
- The only ships in the Empire's fleet with armaments are Imperial Star Destroyers (unreasonable, but simplifies our comparison)
Then in order for the Death Star to be worth half of the firepower of the Imperial fleet and without taking into account the primary laser, Imperial Star Destroyers would need to carry on average only 1.2 turbolasers. Now, I don't know how many turbo lasers each Imperial Star Destroyer has, but I'm willing to confidently say it's more than 2 turbolasers.
If you assume that the Death Star is a higher percentage of the fleet's firepower, than this ratio gets even worse. If the Death Star is 75% of the fleet's firepower without the main laser, than each Imperial Star Destroyer can average only 0.8 turbolasers.
If you begin including other armed ships that the Empire might have in addition to the Imperial Star Destroyer and convert their energy output to something equivalent to what a turbolaser outputs, than this ratio will get even more ridiculous. So, General Dodonna's assertion of the Death Star's firepower being "over half the star fleet" must include the power output of the main laser in order to make any sense.
But what about Han Solo's quote in A New Hope?
Here is his quote from the film:
"The entire star fleet couldn't destroy the whole planet, it'd take a thousand ships with more power than I've-"
...at which point he is interrupted by the arrival of a TIE fighter.
I have issues with quoting Han Solo as evidence that General Dodonna was incorrect or not referring to the main laser in his comparison to the Imperial star fleet's firepower.
Han Solo said that in the moment under stressful conditions.
He's a smuggler and presumably has been for a while, so his knowledge of Imperial fleet capabilities may be suspect.
Thousands of Star Destroyers hitting a planet would result in an overall targeting footprint that is quite wide on the planet's surface while the Death Star's laser is highly focused. Compare normal summertime sunlight (multiple Star Destroyers), and then focus it using a magnifying glass (Death Star). The Death Star can apply more damage with the same energy output, but focus it in tight area, presumably allowing it to reach deeper into the planet and causing it to explode.
Thus, it is likely that the Death Star's total firepower rating includes the main laser. Since Han is thinking in "the number of Star Destroyers it'd take to blow up a planet", and he obviously hasn't found out about the Death Star yet, I find his statement unreliable and General Dodonna's assertion of the Death Star's firepower unreasonable unless it included the main laser's output.