How to correctly use the formula for calculating the air-gap in a pulse transformer?
Perhaps there are other formulas with which you can get the Air gap
value, the desired value of the magnetizing inductance?

Well, you have the ferrite core-set data sheet and you have the ferrite material spec; 3C95 so let's proceed from there. The important formulas to know are these: -
The effective permeability of a core set when gapped
$$\mu_e = \dfrac{\mu_i}{\mu_i\cdot\dfrac{\ell_g}{\ell_e}+1}$$

Where \$\mu_i\$ is the ungapped magnetic relative permeability of 3C95 (2530)
Where \$\mu_e\$ is the gapped magnetic relative permeability of 3C95 (trying to find this)
Where \$\ell_g\$ is the length of the gap in metres (maybe 1mm or 0.001 metres)
Where \$\ell_e\$ is the core magnetic length in metres (0.113 metres)

If you plug-in the numbers with a gap of 1 mm, \$\mu_e\$ equals 108.17 and this is used in the next formula for inductance: -
Inductance of the gapped core set
$$L = \dfrac{\mu_0\cdot\mu_e \cdot N^2 \cdot A_e}{\ell_e + \ell_g}$$

Where \$A_e\$ is the effective cross sectional area in m² (328 mm² or 3.28 x \$10^{-4}\$ m²)
Where \$N\$ is the number of turns (18)
Where \$\mu_0\$ is \$4\pi\times 10^{-7}\$
The formula assumes that gapping has increased the magnetic length of the core - should you in fact &quot;grind&quot; down the centre limb, the total effective length remains as \$\ell_e\$.

So, if you plug in the numbers now (1 mm gap) you get 126.7 μH
Given the above, I reckon you should be able to figure out the reverse process to get the inductance you require (about 2 mm).
Summary
You will also have to double check that you have provided enough of a gap so that the peak magnetic flux density remains significantly less than 400 mT. I usually aim for 200 mT but, in the Cree document that you linked, they appear to be aiming for 120 mT. This is fairly easy to check remembering that \$B = \mu_0\cdot \mu_e\cdot H\$ where \$H\$ is the peak current multiplied by number of turns and then divided by \$\ell_e\$.
Or, \$H = \dfrac{MMF}{\ell_e}\$