The best actually-printed-by-an-inkjet-printer circuits I know of are simple ring oscillators of at most ten transistors or so (e.g., [1]---and they're pretty bad transistors at that), and even the simplest microcontrollers require thousands of transistors.
The paper [2] is a good review of the difficulties. Inkjet printing has at best a ≈20um minimum feature size (vs. 0.01um current transistor sizes), and the material choice is really hard: instead of silicon, you need to make semiconducting inks using funky organic molecules like 6,13‐bis(triisopropylsilylethynyl) pentacene (TIPS‐pentacene). [3] is a good recent paper trying to work around some of these limitations. So everything is still very much in the research phase.
Although inkjet printed circuits won't be anywhere near current silicon circuitry anytime soon if ever (and inkjetting transistors is the best (and kinda the only) method of 3D printing circuits we currently have), the different form factor may be useful. Circuits---even if only a few thousand transistors---could be printed on 3D geometry for interesting microfluidics capabilities, flexible circuits might make good healthcare sensors, and [4] is even studying flexible spacecraft via printed electronics for surprisingly economical space debris removal. And combining all this with 3D printed mechanical parts (via, e.g., the impressive PolyJet [5], which is basically inkjetting layers and lacks only the right materials to print electronics) will be fun.
(as to the source's Air Force Research Lab printed chips, yeah, I can't find further info, either, and agree it was probably sandpapering away most of the spare silicon bulk of an integrated circuit [impressive, useful, but not printing])
The paper [2] is a good review of the difficulties. Inkjet printing has at best a ≈20um minimum feature size (vs. 0.01um current transistor sizes), and the material choice is really hard: instead of silicon, you need to make semiconducting inks using funky organic molecules like 6,13‐bis(triisopropylsilylethynyl) pentacene (TIPS‐pentacene). [3] is a good recent paper trying to work around some of these limitations. So everything is still very much in the research phase.
Although inkjet printed circuits won't be anywhere near current silicon circuitry anytime soon if ever (and inkjetting transistors is the best (and kinda the only) method of 3D printing circuits we currently have), the different form factor may be useful. Circuits---even if only a few thousand transistors---could be printed on 3D geometry for interesting microfluidics capabilities, flexible circuits might make good healthcare sensors, and [4] is even studying flexible spacecraft via printed electronics for surprisingly economical space debris removal. And combining all this with 3D printed mechanical parts (via, e.g., the impressive PolyJet [5], which is basically inkjetting layers and lacks only the right materials to print electronics) will be fun.
(as to the source's Air Force Research Lab printed chips, yeah, I can't find further info, either, and agree it was probably sandpapering away most of the spare silicon bulk of an integrated circuit [impressive, useful, but not printing])
[1] https://doi.org/10.1021/acsnano.6b06041 [2] https://doi.org/10.1002/admt.201700063 [3] https://doi.org/10.1038/s41598-017-01391-2 [4] https://www.nasa.gov/feature/brane-craft/ [5] https://www.stratasys.com/polyjet-technology