They do appear to mean emulator.

The PDP-8 was hardware replicated many times. In the '80s it was a common final year project. There's a classic textbook that works through designing and implementing a clone of the PDP-8/I [1]. I've run into a number of threads over the years where hobbyists have done it with TTL to varying degrees of completeness.

The Apollo Guidance Computer was recreated by a hobbyist from the original designs using a modern logic family but gate-equivalent -- and I can't find it online anymore! Anyone know?

You can still build an original Apple II. [2] Being from the late 1970s there was no custom logic; it's straight TTL plus a 6502, and all the chips are still in production except for the ROMs and DRAM, which are easy enough to work around or find used.

[1] https://www.amazon.ca/Art-Digital-Design-Introduction-Top-Do...

[2] https://www.reactivemicro.com/product/apple-ii-plus-rev-7-rf...

replica / new hardware that looks the same, with lights and buttons. Behind the panel is (from the one I looked at) an Arduino running an emulator. Don't know if the blinking lights respond the same or if the hardware switches, ports, etc work.