Real-time in computing usually either means a real-time OS with guaranteed low latency response (typically for stuff like microcontrollers regulating machines) or streaming live data (low latency delivery of the most recent value)

This sounds like the latter, and a typical SQL database don't guarantee real-time updates (you can have "atomic writes" to prevent inconsistency but usually this would make it slower) but some databases like this one are designed to ensure you can read out updated correct and consistent values much faster. Also with standard databases you usually make scheduled individual requests, but a real-time database could often send a stream of updated values to a "subscribing" program

Sounds like someone glued redis to MySQL and branded it.

An SQL database that is made to deal with real-time data such as player positions. I'm not sure if this is the official term for it, but I think they call it that and it seems to fit.