1. Where you say "the company revealed that Mantle, it's ambitious attempt at a 3D graphic API to rival DirectX and OpenGL," this statement is not completely accurate. D3D and OpenGL are High Shader Language APIs. AMD Mantle is not an HSL API. It is a CPU-GPU Optimization API with additional perks. So you can't really say they are the same, and you can't make a claim that it is AMD's rival-API when AMD hasn't released or announced a HSL version.
2. The 45% isn't 45% to all setups. It's 45% for an APU setup. Mainly, this is with the Kaveri APU. There could be a possibility it will be less than 45% with Richland or below. Also, there's a possibility that it could be higher with bulldozer, Haswell, Sandy Bridge, Ivy Bridge, Ivy Bride-E, Haswell-E, etc...
The Starswarm Demo showed the game without AMD Mantle, running at roughly 20 ms per frame, or 49.99 FPS. With AMD Mantle, the demo was running at 2 to 6 ms, or roughly around 200 FPS.
If you watch the following video, I believe there is some accuracy to this to an extent. It could be fake. Who knows for sure at this current time.
I suspect there is a group of people who are testing the AMD Mantle Beta Version with BF4, and this person is one of them. Take into account, when you watch this, towards the end of the video, this person is using GPU-Z. He hints two things. One, I believe he is using a Haswell setup. GPU-Z shows the integrated Intel Graphics 4000. Two, he's got a R9 series for his Discrete Graphic Card. Since Haswell has 4 cores at a higher Core Frequency, it's possible that FPS performance will go up based on the amount of cores your CPU has, and it's core frequency.
Since AMD Mantle requires a driver on the users end, the person in the video enabled the AMD Mantle in the AMD Catalyst Client. So, in my opinion, it's looking less fake.
If 45% is what AMD Mantle offers at 162 to 200 FPS, then the Kavari APU alone is pushing somewhere around 113 FPS without AMD Mantle. From the video, 300 FPS to 400 FPS is more than twice. Now if you increase the amount of cores on the CPU, this 45% will probably start to show some form of diminishing returns, but the FPS will go up higher. Why is that. Well for a start, AMD Mantle, for a lack of a better term, redirects commands through the other cores for the GPU. Thus, reducing the CPU Bottleneck occurring at the first core.
What's the point in having such a high FPS. If you look at it in context when benchmarking "Video Graphic Cards," high FPS performance versus Game-A, B, C, D, etc, is the x-factor. If AMD can provide their products with AMD Mantle, they can push higher fps for top-selling, PC Games. Higher fps equates to higher popularity versus brand B Graphic Card, and revenue returns go up as consumers purchase "higher-performing" products. Marketing of Graphic Cards are heavily dependent on third party benchers like Techpowerup.com...