Most modern laptops have more than decent audio output, but if more quality is needed one could buy a small external sound card for a lot less than €100.
This one for example would fit easily in a notebook bag.
https://www.thomann.de/gb/miditech_audiolink_light.htm
About the article circuit, I 'm not that sure the 5532 is a good part for headphone amps, unless the phones have a high impedance and resistance: they're intended as preamplifiers (and very good ones) so they hardly can supply the current to fully drive phones, though I guess they can still be ok for listening to soft jazz in a quiet room:)
Regarding the op amp selection, he just used them because he had them lying around.
"If you wanted best possible sound you'd use some actual audio op-amps rather than these cheap NE5532P. And buffer the output of the op-amps somehow. But of-course size and cost balloons if you start adding buffers and stuff."
What I like about his project how he simply used a couple magnets to hold the lid on. Microsoft did something similar on my keyboard, but I don't know that it is something used much on DIY projects like this.
About the article circuit, I 'm not that sure the 5532 is a good part for headphone amps, unless the phones have a high impedance and resistance: they're intended as preamplifiers (and very good ones) so they hardly can supply the current to fully drive phones, though I guess they can still be ok for listening to soft jazz in a quiet room:)