That's correct.
Typically, once I finish working on a game, I sell the final version for a one-time payment. Future updates won't require you re-purchase the game as long as you download it from the same account you bought it from.
There's also a special discount going on until at least Apr 15th. If you pledge $5 on the House Chores Patreon page and link your itch account to it, you can download the game at no additional cost to save $2!
Once I start working on the next game in the House Chores 'universe', that game will be free to play throughout the early development of it.