Yes, the principle generalizes. If all the LEs are positive, then the Lyapunov dimension is equal to the number of variables (and LEs).

Yes, the calculation of Lyap dim procedure is quite evident. But I wish to know its value when all LEs are positive.

Yes, you got it right that the mentioned LE values are from modified 2D Henon discrete map. We have a number 2D discrete maps available in literature where both LEs are positive, like

Article 2D Logistic-Sine-Coupling Map for Image Encryption

https://ieeexplore.ieee.org/abstract/document/8684083/

Article A novel bit-level image encryption algorithm based on 2D-LIC...

Jefferson, Whats your opinion about the mentioned case?

Assuming the system is bounded, I agree that the Lyapunov dimension would be 2.0. A simple example is two weakly coupled chaotic logistic maps. See http://sprott.physics.wisc.edu/chaos/2logmaps.htm

Dear J C Sprott Sir, Thanks for your words and confirmation regarding the LD of above mentioned 2D Henon map. Yes, the system is bounded.

I also wish to know your comments for (1) n-D (n>=2) hyperchaotic bounded discrete map, Would it be 'n' in this scenario in general?

Yes, the principle generalizes. If all the LEs are positive, then the Lyapunov dimension is equal to the number of variables (and LEs).