Yes, new code requires Tamper Resistant plugs.
Any new installation (anywhere, basement or any other floor) require to use those TR plugs. Your existing installation will be grand-farthered. If you plan to have your wiring inspected, you can't use those none-TR plugs, or you will not pass the inspection. If you never intent to have inspection, then....
If the plugs from LZ are TR plugs, you will be fine.
BTW, the wiring inspection is done by ESA, not city.