Welcome to the Forum ishanmitra. An interesting idea. It is not a holographic system -- holography is based on interference between mutually coherent light beams rather than simple projection (see the Wikipedia article on holography for all the gory details

). The method you are considering has the advantage that it places fewer demands on the apparatus used than would holography.
I foresee a problem however. I'll denote positions in the image by cartesian coordinates {x, y, z}. Now consider one horizontal slice through your 3-D image, at, say z = 0, and suppose that you wish to illuminate spots at {1,1} and {2,2} (where I have dropped the constant z term from the coordinates within this slice). The first spot requires that beams at x=1 and y=1 be turned on so that their intersection at {1,1} is bright. Similarly the second requires beams at x=2 and y=2 be on. The problem is that now the spots {1,2} and {2,1} will be illuminated brightly, even though these positions are not part of the desired "image" of dots at {1,1} and {2,2}. In a more realistic case of "drawing" a line connecting the two dots, we would have all the beams on over the continuous ranges x = 1 to 2 and y = 1 to 2. The spurious images would now fill a square with corners {1,1}, {1,2}, {2,2}, and {2,1}, which totally obliterates the desired line.
Offhand I don't see a way to fix this problem, but that absolutely does
not mean that there is no solution. Goodgle luck!
"I have not failed. I've just found 10,000 ways that won't work."
Thomas A. Edison