My question is why does light move in such a way rather than vibrating or rotating, or any other actions, in-situ? Is it due to absence of Higgs boson or perhaps I should ask why does not all elementary particles move in a straight line?
You have managed to mix two different frames of reference in the above paragraph. Light belongs to the classical physics frame , classical electrodynamics with Maxwell's equations, classical mechanics, thermodynamics and statistical mechanics. The Higgs boson belongs to the frame of quantum mechanics and elementary particles. In this frame the carrier of electromagnetism is the photon, an elementary particle in the standard model of particle physics.
The elementary particles in the table are point like particles, i.e. they have a probability of appearing whole at a point in space time ( x,y,z,t); probability because they are quantum mechanical entities really, the probability describing their evolution is expressed by a probability wave, the square of the wavefunction, the solution of the quantum mechanical boundary value problem.
So a single photon by itself will give a point (x.y) on a photosensitive screen at z, and a track can be extrapolated from the source to the point(x,y), except that the probability of finding a specific point(x,y) on the screen has a wave like functional dependence. And a photon moves with speed c.
Light can be shown to be built up by zillions of photons in a mathematically consistent way at the limit of large numbers, light is an emergent phenomenon from the underlying confluence of many individual photons. .
The existence of three dimensional holograms should satisfy you that all sorts of shapes can be built up by light, the continuous flow from the source ( laser) of zillions of photons. Individual photons cannot be static, they go to infinity or interact and are absorbed and scattered, keeping the velocity c.