Oppo research firms are basically paid professional stalkers who hire licensed private investigators. Private Investigators have access to advanced databases that are used to track down people that are hard to find, and they subscribe to other databases that they can consult to get a better idea where the guy lived and worked, and who he hung out with, in his adolescent and adult life. The stalkers and private investigators use these clues to make educated guesses about where he would hang out online. In many cases, the phone number used to sign up for an e-mail service, and the e-mail address he used to sign up for a social media account, will come from licensed private investigator's databases.
That helps narrow down where to look. Even if Platner had deleted his digital footprint, his ex-coworkers and drinking buddies probably haven't, and if you download their entire social media and feed it to an AI, the AI can figure out when those friends are tagging or talking about Platner. If any of those "mentions" revealed a potential screenname, that's an investigative lead for the stalkers to check up on.
If you know his potential screen name, you check the Reddit archives and feed that to an AI. The AI can figure out which comments are consistent with all the other known information about Platner. The stalkers and private investigators review the AI's conclusions and confidently report to their client (Schumer and Mills) that the Reddit comments probably were made by him. The Schumer/Mills team leaks the info to a journalist, who corroborates the conclusions, and the journalist reaches out to Platner's campaign for comment, where he will confirm that the Reddit comments were made by him right before the story runs.
None of the above even requires Snowden-level espionage. Meanwhile, the stalkers and PIs have already reached out to people from different periods of his life, learning as much as they can about where a possible skeleton could be buried. This stuff takes longer to investigate and validate, but they have an unlimited budget so I am pretty sure they are trying to get his ex-friends to check in their attic for old computers from 2004 that could be sent to a digital forensics vendor to retrieve AOL instant messenger conversations from when Platner was a teenager because he probably used the n-word, told racist jokes, and was interested in downloading porn at that age.