It sounds like your potential sponsors are similar to publishers in that you’re hoping to get financial backing from them & they’re hoping to get a return on their investment based on how well your game sells.
A good starting resource is Cameron Davis’ Gamasutra piece, How To Pitch Your Project To Publishers (backup link). The entire article is very good, but a bit long, so I’ve attempted to summarize the parts that seem to most directly address your question:
In order of effectiveness, the best ways to convey your game to your audience are:
- interactive gameplay prototype
- non-interactive video presentation of gameplay
- concept art and environment views cut like a trailer
- spoken presentation with supporting materials
Provide a gameplay walkthrough, from the point of view of the player, describing key gameplay mechanics and event sequences they would experience during a particularly interesting moment in the game. Promote the best aspects of the game, elaborate on the unique selling points.
Don't get bogged down in minor details (features that little or nothing to do with the core gameplay mechanics). If it's a minor part of the experience, your publisher will assume you're going to come up with during the course of development anyway.
In response to the article, Carlo Delallana & Jake May, commented that you need to sell your team as well as the game.
Another great resource is Rami Ismail's presentation from GDC Europe 2014, In 3 Sentences or Less: Perfecting Your Pitch (backup link & transcript). Again, the entire thing is great, here’s a summary of the part that seem to address your question.
The important questions are “the what, who and why,” & your goal is to be able to give fast, concise, interesting answers:
Who are you?
Introduce yourself to get credentials before your audience if they don’t already know you and what you’ve done. Knowing what the audience expects from you is important. Publishers want to know: have you got a team that is dependable?
Who are they?
Know your publisher & what they usually publish; you’ll need to show that your game is good fit with them. How does it fits in their portfolio?
What are you pitching?
Maybe not exactly the game, but something that exists through the game, be it emotional, economical, feelings, history, etc. Construct a sentence that isn’t too long that starts with: The name of the thing you’re pitching is, and finish that sentence. If you’re using more than one comma, you’re doing it wrong.
Why are you pitching that?
This is all about the value proposition. What are you adding, what are they getting they wouldn’t get otherwise? Publishers want to know what will this collaboration bring to the game, that you wouldn’t have otherwise?
Why are you pitching that to them? What does this publisher offer that others don’t? What would they gain from what you’re pitching? What would this gain cost them?
Structuring your game pitch is mostly about time. When done correctly, the value of information you’re giving needs to outweigh the time they had to listen to you. It basically comes to, don’t waste people’s time.
Finally, focus on the why before focusing in the what. Why will players have a good experience from this game?