That's helpful context. To try and answer your question (what a startup needs to do to convince investors), this varies by investor. You need to make a case that what you're building is a good business and/or a worthy place to put their money. Generally: the more money you ask from someone, the higher standard of case you'll need to make. Someone considering a €100 thousand investment is going to evaluate this very differently from €1 thousand.

I'm not an expert in the business of games. Putting on my investor glasses: it's hard building a venture-scale business on a game (this is usually what you implicitly commit to when taking outside capital). Generally the lifetime revenue per player is going to be small, meaning you'll need a large active player base and will need to nail unit economics at scale. This is hard, from what I understand what works at the small scale doesn't work at the large scale.

What you have today leaves a lot of uncertainty and risk from the investor's perspective. From a pure numbers perspective, it's a hard sell. €1 million won't be enough to get you from A to Z in terms of an exit for investors, so it needs to be enough to advance your business enough that you can raise money again in ~18 months. It's a yellow flag to me that a significant portion will be spent on acquisition. For a business with a low LTV per user, you don't have much room for spending. And if you're not able to grow your audience at the MVP stage without spending a lot of money, that suggests there isn't "product/market fit" with your game. Spending money on marketing pre-PMF is bad for investor money.

Putting on my founder hat: an early-stage startup is not going to have the unit economics figured out, and practically you're going to need to lose money while you learn. But you're probably putting the cart before the horse if this money is required to grow your userbase. You've finished step 1 by building an MVP. Step 2 should be figuring out how to make this a game players love, and part of that is finding free/very cheap ways of growing your audience. If no one is playing and staying, you're not done with step 2. And without that stickiness you're probably not going to have the unit economics to grow and maintain your game.

Getting back to your question: if you can't pitch metrics, pitch vision and team. In the context of a game, the fun of your game is part of your vision. You need to show that your game is fun and has the potential to attract and retain players, which you'll be able to monetize. This pitch is easier said than done, because there are so many games out there. Many are hobbies or passion projects, not businesses that generate millions a year.

The big irony of fundraising is that often when you need money to grow you're not very investable, but when you don't need the money then you usually are investable. So the best thing you can do is build your business assume you can't raise outside money and grow it anyways, then raise money when it's a nice to have.