Why does working from an office increase motivation?

This article begs the question. It just assumes that working in an office improves motivation. The article they point to says co-working environments improve perceived productivity, not motivation.

I've worked in a remote job for more than three years. I can say that the most important thing to stimulate productivity is to create clear signals for yourself that you are engaged in work time, not play time. Having a coworking environment is one way to do that. You get out of the house, to a place free of domestic distractions—you aren't tempted to wash the dishes or watch TV instead of working. But you also explicitly demarcate the work portion of your day. You can also achieve this separation by having a work desk/computer and a distinct personal space for games, email, paying the bills, etc.

The other thing that a coworking situation can provide is social reinforcement. My approach to that issue, as a remote worker has been two-fold. First, make an extra effort to engage with your coworkers. Make time for chitchat about life and whatever random crap comes up as well as work related topics, you'd be doing this in an office environment without even thinking about it. Secondly, get out of the house regularly—I found that going and working in a coffee shop or library at least once a week provided a nice change of scenery. If you become a regular, other regulars will come to recognize you, and you can socialize there as well.

Humans are creatures of habit. We respond strongly to various cues that let us know what we are doing at any given time. Wrapping your work life in a set of ritual activities and signifiers that distinguish it from your personal time improves focus and productivity.