"I can analyse others and share my observations/opinions. That doesn't require any specific qualification."
Are you more able to do so than others on this forum?
Everyone is capable of sharing their observations/opinions as much as each other.
"Moreover, would you say that this ability to "read people" extends to this (primarily textual) context?"
No. Online your limited to the information you're presented. Of course, not everything is always as it appears. Sometimes it's a matter of reading between the lines and interpreting the message. Everything expressed can give some insight into the author's mind.
In real life you're presented with more visual information, which makes reading people that much easier (not that it's hard to do online either mind you).