What is there now is an height-adjustable pintle meant for something definately not as heavy. The whole gate rests on the ground.What I suggest is a six-inch pintle that is set in after drilling a hole through the pipe which, if sheathed in another tube during casting, can be adjusted horizontallly by merely screwing, or unscrewing a nut on its machine threads. It might be tricky chipping away at the existing concrete of the old poles, perhaps requiring temporary removal of the wood posts as well, but to hold the weight of what is intended extra strength is required.
It should be noted that the vertical sides of the gate itself should also be replaced with either a four by four, or two two-by-fours sandwiching the female part of the hinge strap. If set in an overlay position bolstering would need to be done on the oustide part of the gate.
On the backside I suggest one of those new galvanized "hat channels" made for restoration of old cedar privacy fencing that have perforations all along the bottom edge. This would be cut to fit in the gate diagonally. The existing gate has a small cable now which doesn't seem to do anything.
The last feature is the installation of a cane bolt into the ground. What I've seen work is a single piece of 3/4" pipe driven into the ground where the other half of the fence is bolted horizontally to the fixed unit. The 5/8" cane can even be lengthened to the height of someone on horseback so they don't have to dismount to get through the gate.