You don't "puff" a cigar, you smoke it.
Even if you don't realize it, you are inhaling to some degree. Inhaling does not have to equate to a bong hit to be effective. It can be subtle, and in fact that is one of the beautiful things about cigars: you don't have to consciously inhale to enjoy it, like you would with a cigarette.
But to suggest that you "don't inhale" is a little naive.
When I smoke, I find myself exhaling through both my nose and my mouth, allowing me to capture the entire spectrum of the flavors and aromas. It's something I've done since Gael at La Luna cigars suggested for the African Fuerte. I've been doing it ever since, and I highly recommend trying it.