remarkably similar theme and structure
Shared inspirational source maybe. Could be indirect through several steps.
Also, there is the genre aspect of many games. One will always find common ingredients or ways to categorize and group games together. It is also the concept of tropes (plot devices).
It could also be as simple as you not having encountered this type of game concept before, and the concept not being as unique as you thought it to be.
Is it a secret, or can you share the core tropes? This might be fun. You name the tropes only, and people would tell you games that have those.