This is collision damage, not explosion damage.
Bombs in BotW don't actually blow each other up, they knock them away, because bombs aren't "breakable", like crates and boxes. This also explains why mobs can kick them, or why you can knock them around, without them blowing up.
The windbomb technique doesn't hit Link with the explosion, it hits him with the second bomb, that gets launched by the explosion wave of the first. The reason Link doesn't get hit by the explosion is because the physics of hitting Link with the second bomb sends him flying faster than it does for the blast wave to hit him.
This also explains the difference between the damage of a successful and unsuccessful launch - they hit Link’s hurtbox differently, causing a different "impact" between the bombs’ hitbox, and Link’s hurtbox. ( I won't go into the specifics about it now, I will add this later if need be).