Earlier quoted context omitted.
Hah. Nope. A career where you can make money and move up over time is not low status. Try being a blue collar member of the working poor, or someone deep in debt from a useless degree working a dead end service job. Software is a very cushy job compared with what more than half this country has.
It's the lowest of the white collar jobs.
It is true though that its easier to climb the ladder via social/soft/people skills and selling/positioning yourself well and knowing who to associate with etc. compared to working real hard on technical stuff. If you want to impress general people, tell them about people related achievements, like how you led a big group to success, or how you resolved conflicts, big names you've worked with and know etc. Social capital is indeed more valuable in general and so managers and "soft" professionals like lawyers can seem higher status. But its more about the focus on people vs things. Rule of thumb: if you can be objectively wrong or make an objective mistake, you're on the lower end of status. If situations are more wishy washy and rhetoric can save you, you are higher up.
Even though formulating it bluntly is frowned upon: as a software engineer you dominate (rule over) computers and equipment (similar to blue collar work), but to get respect from non techies you need to dominate people. No way around it. That's why managers like to have many reports, even if they are useless and hurt the bottom line.