Actually, this blog post makes the story clearer:
http://nikhilism.com/post/2016/systems-we-love/
It isn't a physical IBM 7074.
When it came time to migrate from 7074 to S/360, rather than rewriting their 7074 software, they just wrote a 7074 emulator for S/360. And, it sounds like, they are still running their 7074 software, under their 7074 emulator, most likely on a recent z/Architecture mainframe.
The article makes it sound like people still use "1960s mainframes" when I very much doubt anyone is still running 1960s hardware in production. People use modern machines–modern IBM mainframes, which are multicore 64-bit processors–or other mainframe vendors such as Unisys or Fujitsu use mainly I believe x86-64 running Linux running a software emulator for the old mainframe CPU.
A lot of legacy, sure, but I think this article makes it sound even more legacy than it really is.