I'm afraid your presupposition might be off. The largest number of games must have been played online. Most of them are bullet and blitz games with time controls from 30 seconds per game to 10 minutes. Sometimes with an increment of 1-5 seconds. The number of such games played everyday online is hundreds of thousands and even millions, as there are many websites where they can be played. Online bullet/blitz chess has existed for more than 10 years, and it's going to be dozens or perhaps hundreds of billions of games but I cannot give you any exact number. The number of non-online games is much smaller. The number of tournament games that are in the database for all time is around ten million games. This number is rising fast. That includes correspondence, official tournament blitz games, some non-tournament games, and some official online tournament games, etc. The overall number of OTB games played by humans over centuries must be much higher, probably hundreds of millions and even billions of games but definitely not as many as the number of bullet blitz games amateurs have been playing online. Nowadays many amateurs have played more than 10,000 games online! The number of amateurs is many hundreds of thousands and even millions. Besides, in modern times you can play even on the phone. Just one website (Lichess) has created a database of their online games and it's more than three billion games over several years. Unless major portals, like Chesscom, Chess24, ChessBase, Lichess etc. provide exacts statistics the overall number is just a speculation. What's more, there are many hundreds of other portals where people play chess, some of such websites are not dedicated only to chess.
It's important to note that even many OTB games have been played recently as blitz games with the advent of the chess clock. There must be over one thousand chess clubs around the world (a very rough guesstimate). At an average chess club, dozens of blitz games are played daily. It means thousands of blitz games are played daily in chess clubs around the world. Over 50 years' time, it's got to be dozens or perhaps even hundreds of millions of games, but nobody knows exact numbers since there's no statistics of that sort. And that number might be even comparable to all non-blitz games played throughout the history of the human race by amateurs. What the latter have played is close to rapid chess. We can only speculate as to how many games amateurs have played over the centuries. Perhaps, hundreds times more than our database of ten million games. That means billions of OTB games by amateurs throughout the history. It's important to understand that the number of amateurs is roughly thousands of times higher than the number of professionals. However, an average professional used to play dozens of times more games than an amateur did. As I already said, nowadays amateurs play thousands of games online. Many professionals eschew low quality online games and/or don't strive to play too many blitz/bullet chess games online. So, it's been a huge avalanche of online blitz/bullet games by amateurs over the recent decade or so. So much so that some amateurs have played more games than some professionals!
Additional remarks:
A note regarding chess clubs: There are very big ones where hundreds of blitz games can be played daily. And there are very small ones in some podunk towns which might be closed most of the time with very few players who play there.
Most of online rapid games are actually blitz games by pro standards by FIDE, i.e. they are too short, like 10-15 minutes. The standard for the rapid game was 25 minutes and with the advent of the digital clock with increments it has become 15 mins + 10 second increment (equals 25 mins for 60 moves). Increments have been in practice for around 20 years now. Amateurs often play without increments or even without clocks when they play OTB. Cheap chess clocks without increments (like analog clocks) are still manufactured and sold worldwide. It's logical to expect that amateurs play mostly blitz games with clocks just like they do online. As to long games, mostly only professionals play them. They are also with increments nowadays but overall it's around 2-3 hours for White and and the same time for Black per game. What amateurs play without a chess clock is also like a rapid game, usually faster than 30 mins per side. Amateurs don't play serious chess as a rule.
