From Simons_Nicolai’s link above:
However, live subtitling, as seen mostly on the news, sporting events and other programmes which are going out live, requires an entirely different skillset – a person with good ears, a clear speaking voice and specially ‘trained’ voice recognition software.
These live subtitlers sit in a soundproofed room, watching the TV feed and ‘re-speak’ the words from the programme clearly and deliberately into a microphone. The computer, which over time has come to accurately recognise the live subtitler’s voice, then translates their spoken words into text on screen.
Stenographers are sometimes used but, for the most part, this is how live subtitles are generated. A lot of time and effort goes into training the voice recognition software to as high degree of accuracy as possible, and into augmenting this with subtitling software which tries to pre-empt foreseeable errors. Unfortunately, given the infinite variety of the English language, human error, commentators misprouncing words, the subtitler mishearing or stumbling verbally, having a cold which makes your voice sound different, and the fallibility of the voice recognition software, occasional unforeseeable errors do creep through. Corrections are made where possible but sometimes, overall, more information is lost to the viewer during a live broadcast from stopping to make a correction than from just keeping calm and carrying on.
The subtitles for the web clip above will have been produced for the clip viewed on the web, not the TV version, presumably done by the programme production team who do also the graphics which tell you people’s names and locations, etc.
Subtitlers are mostly rabid pedants and grammar Nazis who would hang themselves with their headphone lead at the end of their shift if they thought they’d broadcast a sentence about break leavers.