Why is this IDT6116 SRAM chip overheating?
The Alliance AS6C6264 memory part has a Voh of 2.4V, with the IoH being -1mA or 2mA.
The IDT6116SA/LA has a Voh of 2.4V, with the IoH being -4mA or 8mA.

So typically the output voltage of the IDT could be higher. An LED's IV curve is exponential, so if you give it a little more voltage, you get a lot more current. So I believe what is happening here is the IDT part is sourcing much more current and burning up much more power.

Increase the current limit the LED's (or remove them, yeah its cool to see the data go by but useless) and the problem in all likelihood will go away.