If the second card is running at x4 - yes, performance will be limited.
If both cards are @ x4, performance would be even further reduced.
But that board you received should be running at x16/x4.
Either way it would be lowering your frame rate a fair bit and since it's not what you ordered, I'd ask for the right board or a replacement.
x16/x8 is fine - x16/x4 isn't