This would be true if the turbos perfectly compressed the air with no increased heat. But in reality, 88% higher pressure does not mean 88% more air molecules. I used 60-65% which gives you around 225-230hp.
You could run the engine without boost and measure IATs, then again with boost, to better estimate how much air you're actually adding, but at that point you might as well just dyno it without boost.
Fellas, the calculations are solid, it's a 200 hp NA engine.
The engine has an intercooler which removes heat from the compressed charge. A best-case scenario for an intercooler's efficiency is cooling the the charge to 10-15 degrees above ambient.
You are simply guessing with your 60-65%. In principle of course you are right regarding the effects of heat, but that is what an intercooler is for, to remove the heat and make the charge denser.
Therefore, the physics behind the calculations stand:
NAhp x Boost = BoostedHp
200hp x ( 1 + 13psi/14.7psi) = BoostedHp
200hp x 1.88 = 376hp
BTW, excellent response regarding the differences between an engine built strictly for NA versus one that will be boosted - as you pointed out, they are NOT the same engines despite being the same displacement.
AND, this is why I would choose an NA V6 300hp versus a 4-cylinder boosted to 300hp. At cruise and not under boost, that 4-cylinder is less efficient under those circumstances due to amongst other things, a lower mechanical compression ratio, thus lowering the engine's efficiency and lower fuel mileage as a result.