I'd have to look it up, but I'm pretty sure that the open loop gain for the 324 is at least 1,000,000, and that's voltage gain. With an op-amp you look at the gain-bandwidth product. If it has a gain-bandwidth product of 1,000,000 you get a DC gain of that much but only 1,000 at 1,000 Hz. A project like this is happy with any op amp that can swing close to the supply rails. The current gain of most op amps is "very high."
The gain issues with this project have to do with the amount of current the resistors let through the transistors. With a 12 volt supply, not more than about 2 milliamps can get through to the bases of the driver transistors using 4.7k resistors. The current gain of those transistors will be about 100. The power output transistors will have a gain of about 50 to 100, and I would measure that before using them. It will take 100 milliamps to the bases of the output transistors to get five amps through them, or 200 mA to get 10 amps through them. It's not quite that simple, but that's a close estimate. Also, at 10 amps the .1 ohm resistors I specified will drop a solid volt each. These specifications are marginal at 10 amps and you won't get more than 9.8 volts each direction. The best thing to do is to reduce the 4.7k resistors to about 2.2k to 3.3k, the 47 ohm resistors to 22 to 33 ohms, and the last current limiting resistors to .05 ohms or maybe do without them. Most op amps can handle 25 to 30 milliamps indefinitely, so the approximately 5 milliamps required will not strain them.
At 1 to 5 amps the values specified should be solid. You can still lower them the way I just said. Doing so will give you headroom. I just picked the values I did in sort of a hurry. Those values are not very critical, but when you are running 200 mA into the bases of the output transistors, you are going to need the current limiting resistors at the collectors of the driver transistors to be able to take at least 2 watts. Those are the ones that are marked "47". An alternative is to use Darlington power transistors for your output transistors.