The claim in the article was "invented in 1947"; a patent is by definition granted for an invention, regardless whether a working device was built or not.
No. It must be novel, non-obvious and "useful", which obviously was considered to be fulfilled by the patent office. The patent describes how the invention can be used instead of tubes.
Those sources appear to exclude Lilienfeld. He didn't create a good or tool. He didn't create a material. He didn't create a manufacturing process or a control procedure or a method of measurement.
Lilienfeld was a brilliant man but he didn't invent transistors any more than Albert Einstein invented gravitational wave detectors.
The patent doesn't mention the term "transistor"; but obviously the patent office came to the conclusion that it is a patentable invention, and the cited by list confirms that it is considered a relevant invention by Bell Labs and other notable institutions. Prior art by Lilienfeld did even stop some applications of Bell Labs from going forward. The transistor invented in 1947 was a point-contact transistor, which is not the concept applied in micro processors as the article confirms.