I think the key here is that the chain made contact with Dropkick during his transformation process and thus became embedded in his systems. Imagine for a second that the Transformers are insect-like creatures, with extremely durable exoskeletons and soft, pliable innards. That exoskeleton would be hard to break (for another insect) unless for some odd reason there was a string that became attached to the insect during its larvae stage and became integrated with its later-developed exoskeleton. Pulling on the string would apply a force in the opposite direction than the exoskeleton is designed to resist, and its integration with the exoskeleton would create fracture points around the point of its integration, thus breaking it much more easily. Maybe a weird way of thinking about it, but that's what made sense to me. I actually thought this detail in the movie was quite clever and I enjoyed it. Don't ask me why Dropkick blew up though, cause I have no idea!