Yet no transaction fee?
Yes, it is a lot like Steem, resource credits {RC} based.
Set some stake.
Every interaction with any blockchain will put a strain on the available resources. There are factors like RAM (memory), CPU (processing) and NET (storage) that are being used. Every transaction has its own type of operations. EOS can add 2 blocks per second to its blockchain. Each having transactions in them with certain operations running. The more of these per block, the heavier it weights on the resources of the blockchain system. That will have its reflection on the EOS based stake price of the needed resources for every single interaction.
With HardFork 20 Steem got their own system installed, known as Resource Credits {RC}. At first it was set at quite a low amount. After which it was almost impossible to interact with the Steem blockchain. Although it was experienced as a very unpleasent experience by many, it did unintendly show how stake determines the usage limits. When it gets set to high, meaning you need to have a huge amount of Steem Power at stake, only a few can post, reply, vote and so on. Finding the right levels is very important in a resource based system.
The resource market
One thing that can put an extreme unwanted strain on an information storing blockchain, like Steem, is SPAM. The same accounts for EOS and a lot of other blockchains out there. Even the Bitcoin blockchain can be flooded with useless low value transactions, not paying a transaction fee. Delegated Prove Of Stake {DPOS} based blockchains can put a limiter on that, in a more effective way than Proof Of Work {POW} ones can.
Supply and demand can be used on a DPOS system to keep the strain on the blockchain system under control. Meaning that also SPAM accounts need to put in enough of their own skin. And the more it tries to flood the blockchain with its SPAM, the more resources it needs to put at stake. Finding the right resource limiter settings might take a while, but I think at the long run it will adjust itself almost perfectly. That accounts for the Steem Resource Credit system too.
Not really gratis, but still free
It is always possible to pull the tokens put on stake back out. This means less influence on the blockchain system of course. Unless the demand drops, so less stake is needed to interact with the blockchain. It can also turn around in the other direction, where higher demand needs more tokens to be put at stake. Then the user decides if it is worth investing more, or not.
While the user, group or company, has enough skin in the game, they can interact with the blockchain without any apparant transaction fee. In reality though there is a resource usage charge that an account is being credited for. With Steem this resource usage limiting system does work like a self recharching accumulator. Like Whaleshares uses Mana, Steem uses Resource Credits. (And still has Voting Power, for some reason unclear to me, as a seperate and intregrated(?) resource usage limiter.)
True transactions
There are these false claims being made in the cryptos realm that the 24 hour transaction volume for EOS is fake. Just like for the other DPOS based blockchain systems that have free, but not gratis, transactions. These transactions do come at a price, but they are settled by the use of a stake system. Where one could even argue that the price is payed for with the build in inflation.
No matter what though DPOS based blockchains proof they are ultra fast and can scale easily. Unlike Ethereum that seems to choke on kittyfur. Currently the main three DPOS based blockchains do over 6 million real transactions a day, backed by resources put in stake. While not even braking a drop of sweat. And Ethereum can not even do 10% of that and has to deal with unconfirmed transactions...
It seems to me that those who claim EOS has mostly fake transactions, because they are 'free', does not understand how DPOS functions. Ah well, what else is new... To me it is the most clever blockchain system so far. Now, when can we get to only using the Resource Credits at Steem and lose the superfluous Voting Power thing...?
Transaction fees still has Ethereum chocking on kittyfur.

Screenshot taken at http://blocktivity.info