Hey Gregoriusz,
Eterna uses a handful of what are called “energy models” or “folding engines” to predict what structures a given sequence will fold in to. Integrated into our game are: Vienna 1.8.5, Vienna 2.1.8, NUPACK 3.0.4, EternaFold (a version of CONTRAfold trained on Eterna data), and Linearfold (using Vienna2, CONTRAfold, and EternaFold parameters). Vienna and NUPACK use thermodynamic “nearest neighbor” parameters (IIRC Turner 1999 for Vienna1, and Turner 2004 for Vienna2 and NUPACK. Contrafold and Eternafold are machine-learning-based/probabilistic models. Nearest Neighbor Database is a good reference for the nearest neighbor rules (though there is some subtle differences in how the engines actually implement them.
For a more approachable introduction to Eterna’s gameplay/dynamics, I highly suggest giving A Gamer's Guide to Eterna by player rna-key a read!
Let me know if there’s any other clarification I can provide 