I had a similar experience to the one you describe with some other game I will not mention, and ended up thinking about it in similar terms as you do.
As Bálint says, it is a double edged sword. Yet that does not mean you cannot get ahead.
What happens when they play the game for an online audience, then that audience gets to know the game. If this were people who would not have known about the game otherwise, they are people who would not have bought the game anyway. Thus, you should not think about this as a loss, but as a missed opportunity.
To exploit that opportunity, you need to sell replay value during the gameplay. After all, most "let's players" (for lack of a better name) will rarely replay a game (most of them have to move on to something else to keep their audience interested), thus having multiple endings or stuff locked behind a complete play through will make it harder for them to present the entirety of the game.
Now, replay value is usually achieved with some variation of choice and consequence, yet that could be harder in a story heavy game as those tend to be very linear. In that case, I would suggest catering to theories. How? You avoid heavy exposition in the game. Let the explanations, backstory, setting, lore, mythology and the rest of the world building to those who want to look for it, and make it as deep as it need be.
Do that correctly and “Let's players” will complete the game and only scratch the surface of what the game has to offer. If people watching them find mysteries in the game, if you inspire curiosity, and if people would like to take the control of the game and go explore more by themselves, then most of the work to sell the game has been done.
In abstract, you want to provide joy of discovery, and if you put a lot to discover, “let’s players” will not discover it all.
I fear some big youtuber will play my game, a big portion of my potential playerbase will see the story and not be bothered to buy the game themselves. I mean, why should they if they've seen the story?
Well, it is not that they "should". Yet, they can be interested in playing the game by themselves if:
- They have not seen the whole story because that is not necessary to complete the game. Perhaps you can replay the game with a different character and get a different point of view.
- The story is not the only interesting thing of the game. There is a lot of world building beside the story. Then there are the game mechanics that could (and arguably should) be fun and interesting by themselves.
You might be interested in Shandification. The act of telling a story is also the act of picking what is relevant and what is not... there are multiple way to tell the same story by merely changing the point of view. If you can accommodate that in the game and let the player choose on what to focus on instead of dictating it, then you have the potential to make every play through different.
You may even make that literally. For example, the game "Revolution 1979" lets you take the role of a reporter during the eponymous 1979 Iranian Revolution. Although this means that the player is not the protagonist of the history, it allows the player to explore different parts of the history as it unfolds. This allows circumventing the problem of placing the player in command having player action result in something different that the actual history (by being a glorified spectator, you are not in position to change historical events).
See also How a Japanese Indie Studio Kicks Bethesda's Butt at World-Building
Consider also that the experience of playing the game is not the same as watching it. Of course, this is more relevant for an action games (platforming, first person shooting, etc.) - You need to know what you are making, is it a graphic novel or a video game? Consider games like Chrono Trigger, Fallout or your pick of the Final Fantasy series... they do a great job in storytelling and world building, yet they have game mechanics that are (most of them) fun to play regardless of the story.
On the other hand, if you are making something like a detective game, I suggest to find ways to mix things up, so that it does not play the same every time. Crime mystery really suffer in replay value once you know who the criminal is.
Should I look for other ways to monetize my game, just to be sure?
Yes and no.
Not all games fit all monetization schemes. Some games work best in a pay upfront model. In addition, monetization is better when you considered an integral part of the game design (because it can make or break the game).
On the other hand, thinking of ways to monetize the game (even if you end up not doing it) would be a good exercise to find aspect of the design that you could change. For example, if there is a part of the game that could be different thanks to DLS or micro-transaction, that part of the game that could be different, period. If you can make it so that it plays different every time, you have added replay value to the game.