The range of electromagnetic waves and gravitational force is infinity and the particles exchanged during these interactions are photons and gravitons respectively. Both are massless following the relation: the range is inversely proportional to why.
Then why are the intermediating particle (gluons) massless in strong interactions (as their range is in fermi)?
The important difference is: gluons are charged (carrying color charge and anti-color charge, e g. $r\bar b$) while photons are not charged (zero electric charge). The resulting gluon-gluon interactions make it effectively a short-range interaction in spite of the gluon mass being zero. In contrast to this there are no photon-photon interactions, and that is why photons can propagate infinitely far.
Quoted from Gluon - Confinement:
Since gluons themselves carry color charge, they participate in strong interactions. These gluon–gluon interactions constrain color fields to string-like objects called "flux tubes", which exert constant force when stretched. Due to this force, quarks are confined within composite particles called hadrons. This effectively limits the range of the strong interaction to $1\times 10^{−15}$ meters, roughly the size of a nucleon.
Other people correctly answered how, although gluons are massless, their range appears to be very short. This happens because unlike photons, gluons have (color) charge, and therefore interact among themselves, and create color confinement.
A separate question is why are gluons massless. Well, all gauge bosons - photons, W/Z bosons, gluons, all start out massless. Higgs mechanism causes the symmetry in the Higgs field to generate excitations ("Goldstone bosons") which merge with some of the massless gauge bosons to create new particles - the W/Z vector bosons (massive), the photon (massless) and the Higgs scalar boson (massive). The gluons are unchanged by this mechanism (they do not have electric or weak charges, so they don't interact with the Higgs field), so they remain massless.
I do not think photons or gravitons are massless because their range is infinite, this is not the reason, rather consequence of lack of self interactions between them. Conversely $SU(3)$ gauge theory has immediate consequence of self interactions between gluons and confinement. The massless nature is coming from the $SU(3)$ and lack of presence of mass generation mechanisms. This is same for any $U(N)$ gauge thoery.
