It may feel a bit weird the first few times, but eventually it feels very natural. Nobody cares. Same thing for traveling. The only place where I don't like to go alone are bars. It's boring and it feels a bit lonely seeing people partying where you're on your own.
I'm more akin to what the author describes: doing it primarily while traveling for work. I usually sit at the bar, have a pint and a basket of some sort of greasy finger food. I'd say 3/4 the time I find myself in smalltalk with others near me, or even the bartender. I'm not an incredibly social person either but I've found practically every experience doing it enjoyable. Doubly so since I'm travelling. Talking with others on their travels or the locals is great ways to find other things to do if you find yourself with the time to spare. Quick Edit: Airport bars are great some of the best for this experience imo. I've met some incredible individuals for the 10 minutes we share a space.