Originally we had an issue with the BloodTNT entity ID missing only on the client side (This caused us to have mismatched entity ID on a server+client).
At line 29 in ClientProxy.java you call some of the register methods but you do not call registerEntityTrackers();. I assume it was meant to be called by the parent init() (CommonProxy.java) but you forgot the line to call super(). I also noticed some other places where calls to super() are missing, including the BloodTNT NBT data save code as well as BloodTNT physics.
The 1.10 and later branches seem to make proper use of super() in the equivalent code.
I understand that the 1.7.10 version is old and I don't expect all of this to be fixed, but the errors in ClientProxy.java make the mod completely break any modpack that it is introduced in (because it will unavoidably cause mismatches in every entity ID from every other mod), which is why I think you should at least address this specific instance of the mistake if possible.