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Australian model TGN16R 2005 Hilux 2.7 petrol.
Does it have an EGR system?

The only gadget/plumbing I can find on the exhaust manifold is a "Air Switching Valve" (Toyota part 25710-75015) and that just sends a rubber pipe to a canister behind the bumper bar which then send a rubber riser pipe to vent to the open air behind the grille.

There is also a simple rocker cover ventilation pipe which feeds to the main air tube before the throttle body.

Otherwise, I cannot see any exhaust gas recirculation apparatus. Can anyone confirm please?

The short answer is no. Not many modern fuel injected petrol engines today use EGR and even some diesel engine manufacturers are moving away from it. However the 2TR-Fe does incorporate an air pump which under certain conditions pumps added oxygen or air into the exhaust manifold to assist the cat converter's operation. To my knowledge the only other "anti Pollution" on the engine is the fuel vent purge valve and canister along with the catalytic converters. The hose from the rocker cover to the intake is part of the crankcase ventilation system, which I guess is also part of the anti pollution system.