There's a difference between old free-to-play, which was based on "entitlements" (purchases that you keep for an indefinite time once you buy them), and new free-to-play, which is based on "consumables" (purchases that you have to make and remake to continue progressing). The old shareware model involved making the first chapter free-to-play and making further chapters entitlements. For example, the first episode of Doom was provided without charge and ended on a cliffhanger. The Ultimate Doom paid entitlement brought three more episodes* ("The Shores of Hell", "Inferno", and "Thy Flesh Consumed"); and the Doom II paid entitlement brought another game's worth of missions. Energy mechanics in newer F2P games, such as "gems" or "berries" or "lives", are different: they force you to wait hours or days at a time to progress if you don't pay, and completing the game within reasonable time requires spending more on energy than a player would have originally spent on a whole game under a pay-up-front or entitlement model.
* Before Ultimate Doom was completed, Id Software sold Doom (registered version), which was the same as Ultimate Doom without "Thy Flesh Consumed".