You do interact with the game - you wander around and explore the environment.
I believe what you're trying to actually articulate is that Dear Esther, unlike many games, is not a game built on a linear progression gameplay mechanism, such that it's difficult to know if you're doing what you're "meant" to be doing, and whether you're doing it right or not.
All of which is understandable but misses the point of the game.
Games don't have to be about linear progression any more than films have to be three-act narratives with neatly closed plots and character arcs. I'm not saying everyone should love it, but I think that gaming as a form of entertainment is worse off overall if you try to dismiss efforts like Dear Esther, Dinner Date or any of the many other weird little sandbox games or other experiments as "not games".
I should also point out that I've not tried the HD version of Dear Esther, as I played the original freely-distributed HL2 mod. I do appreciate that with a price tag comes a higher expectation of the final product, but I haven't seen anything on the Dear Esther listing on Steam (for example) that would mislead you as to its nature. "Abandoning traditional gameplay for a pure story-driven experience, Dear Esther fuses it’s beautiful environments with a breathtaking soundtrack to tell a powerful story of love, loss, guilt and redemption."