Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your fellow is more lethargic than usual and appears to have deep, labored abdominal breathing compared to his usual breathing. It sounds like his appetite is off too.
A decrease in appetite makes sense because cats that cannot breathe well often lose their appetite, either because they have difficulty smelling their food (a cat that cannot smell does not eat well) or because his appetite is suppressed due to poor tissue oxygenation. Cats with a poor appetite tend to eat canned food better because it has a stronger, more enticing smell compared to dry food.
A normal cat has a resting respiratory rate of about 10 to 15 breaths per minute, and one breath is considered the in and out motion of his chest. If he has a rate faster then 40 breaths per minute then he is in trouble.
In most cases cats are so good at hiding when they don't feel well that if an owner can notice that he is breathing abnormally then I am concerned for him.
If he were sneezing, had a fever (rectal temperature greater than 103F) and/or had a nasal or eye discharge then he may have picked up a respiratory infection from the new kitten. But you don't mention any of those symptoms. If he doesn't have a nasal discharge and isn't sneezing then his difficulty breathing is likely related to a problem in his chest or secondary to anemia (decreased numbers of red blood cells).
Can you look at his gums and tongue and assess his color? Normally they will be a nice bubblegum pink. If they are very pale, white, blue or gray in color he is in trouble.
Problems in his chest leading to an increased respiratory include primary heart disease (including cardiomyopathy and heartworm), lung disease including asthma, bacterial, viral, parasitic (lungworm) or fungal infections, a mass(es) in the chest including lymphoma, heart based tumors or carcinomas, or fluid around the lungs (pleural effusion) due to a mass, bleeding, chylothorax or an infection.
Anemia can be secondary to poor red blood cell production, either due to kidney disease as the kidneys make a hormone to stimulate production or primary bone marrow disease, or anemia can be due to bleeding or destruction of red cells due to a tumor, blood parasite or autoimmune disease (body attacks its own red blood cells and destroys them).
If your fellow's tongue and gum color are a nice bubblegum pink them he is in better shape then if his gum and tongue color is white, blue or gray, these would signify he is real trouble and this is a true emergency.
The conditions I listed above are serious and I would highly recommend that your fellow see a veterinarian promptly to have an examination and further testing done based upon his examination. He likely needs radiographs of his chest to evaluate his heart and lungs to start and then further diagnostics based upon those findings. That may include a complete blood count, testing for heartworm and lungworms, aspirating fluid for examination if there is fluid present around her lungs, or blood titers for fungal infections.
In the meantime keep him quiet so he can breathe as easily as possible.
Please let me know if you have any further questions.