About 15ish years ago, this was still a heated and pressing open question: what is the dominant mechanism by which most stars (i.e., low-mass stars) form? This came to the fore in a showdown between the two main hypotheses for stellar formation: gravitational collapse and competitive accretion.
Under gravitational collapse, star-forming molecular clumps, of typically hundreds to thousands of solar masses (M$_{\odot}$), fragment into gaseous cores that subsequently collapse to make individual stars or small multiple systems. In contrast, competitive accretion theory suggests that at birth all stars are much smaller than the typical stellar mass (∼0.5M$_{\odot}$), and that final stellar masses are determined by the subsequent accretion of unbound gas from the clump
For a concise yet in-depth discussion of these controversies, see this paper by Clarke (2006).
Comparing updated simulations (for examples, including more realistic radiation effects and turbulence) with observations essentially ruled out the models of competitive accretion in favor of gravitational collapse models. Since then, this result has advanced further, with some apparent exceptions. For example, a recent study of the Orion Nebula found that accretion may play a role in determining the final stellar masses, but that is not necessarily news - we've known for a while now that accretion can play an important role in stellar evolution. But regarding the question of stellar formation itself, this recent study does not seem to give hope for competitive accretion models, despite the pop sci headlines (or maybe I've misunderstood something here?).
In molecular clouds, accretion may play a role in aiding gravitational collapse, as molecular cloud dynamics is a complicated multi-scale process.
For high mass stars, the situation is ever more complicated, as accretion disks can cause a star or protostar to become gravitationally unstable and fragment into smaller stars. Keep in mind, however, that the IMF for high mass stars is more uncertain than low mass stars, and so we can expect theory of high mass stellar formation to be more uncertain. Note, that the vast majority of stars are not considered to be "high mass."
To the OP's question:
Does it mean that there are other ways by which a star can form? I mean, other than the gravitational collapse of gas and dust?
I interpret the language of the Wikipedia article as an attempt to being fair, in the sense that, gravitational collapse is by far the most likely formation scenario for most stars, especially for stars like our Sun, while leaving some room for unlikely yet possible alternatives in, perhaps finely tuned, regions of the parameter space. Another possibility that is considered are stellar mergers, but this also has issues when confronted with observations, and requires some fine tuning of binary hardening in clusters and interactions with tertiary components and is really only feasible in clusters with just the right density.