"Abandoned" is the legal term given to where the city gives up the street and its right-of-way. When the city "abandons" that street, it gives up control, maintenance, and all responsibility for it. Usually, it is turned over to private interests for development as they see fit. Sometimes, the private entity keeps the street in place and then maintains it.
IIRC, the city has an obligation to the public to try to sell the right-of-way at market rates. I don't recall seeing any cases where some consideration wasn't paid for the street right-of-way.
Right-of-way and road pavement are two different things. There are many road rights-of-way that are dedicated but never opened or improved.
It is likely that the developer of the site approached the city about purchasing the 2nd street right-of-way. There were probably public hearings at the time and a vote by P&Z and/or the city council. At that time, the right-of-way was vacated and the land sold to the developer. Generally speaking, when a street is abandoned, the landowners on either side of the street have first option at purchasing to the centerline. I assume a replat would have to be filed to rededicate the 2nd Street r.o.w.