I believe the origin of the term is from micro-loans.
They became a big deal because while they do little in terms of profit they were of great help in creating capital in a region by giving people with no access to jobs the means to invest in their own job, like buying a sewing machine or a couple pigs.
The loans had no collateral and were essentially profitless, except that they built capital in the area that allowed the region to become a place profit could be made, while basically branding your bank on the population.
The current Micro-transaction is a wierd twist on the idea.
You make a free game because anyone will try a game if it is free, or at least a lot of people will. You build up community and interest in a game by having all those people, then you start nickel and diming them once the community is built.
The idea is the no-profit free to play aspect is simply there to build up a loyal player base that without f2p might never have tried the game.
You are correct that Micro Transactions are transactions, but they are actually the result of a negative profit transaction of a free to play game, similar to the micro-loans idea which has made huge impact in the world. Similarly Micro-Transactions have greatly changed gaming.
Also the other side of the definition is that instead of buying a game, you buy little bits of the game, hence each little thing you buy is a part of one transaction, the amount you pay to play that game.
One of the things you always want to do in capitalism is charge people exactly as much as they are willing to pay for your product, to maximize profit. You can't just charge everyone a different price though, but with micro transactions you can.
For example I backed the game Star Citizen at the lowest level to get the actual game, because I was a Wing Commander nut. I am willing to buy the game and play it, but nothing more will I spend at this point. I know a young man who has pent well over $1000 on that game already. We both got the game, and are both happy with our purchase so far. That is awesome Economics in action.
Anyways I'm not always a fan of how Micro Transactions have affected gaming, but I'm not the money, people aren't chasing me.
If Handelabra can make a bit more money and people are happy to pay it, then that is an economic success. Go for it.