Nope.
First of all, Intel manufactures their own chips. Nvidia and AMD on the other hand contract out their manufacturing to Samsung and TSMC. Intel is not competing for that limited foundry capacity. Note that Samsung and TSMC also produce chips for other chip designers like Apple, Qualcomm, etc.
However, all three are competing for tight supplies of materials like substrate.
And capacity issues won't be solved quickly. Starting a new fab takes over a billion dollars of capital investment and 2+ years to bring online.