In the link see that cyclic C-C structure with a triple covalent bond is drawn with an angle, probably the only way to draw it but why is it drawn linearly in non-cyclic and not like single or double bond? I am wondering about the reason for this not that its a convention.
The −C≡C− is normally drawn as linear about each C atom as that is what is found in nature for most alkyne x-ray crystal structures. We can use hybridization theory to explain this as the C atoms would be expected to adopt an sp hybridization, which gives two hybrid orbitals along the axis of the p orbital hybridized with the s to make the sp hybrids:
These orbitals will then overlap with orbitals on adjacent atoms to make two sigma bonds in a linear arrangement about each C atom, giving alkynes their overall linear shape: https://chem-is-you.blogspot.com/2012/09/organic-chemistry-for-level-structure.html
Cycloalkynes tend to be strained molecules as the ideal bond angles of $180^o$ about the alkyne C atoms are not consistent with a small cyclic molecule. This causes cycloalkynes with less than 10 C atoms to have measurable strain and the strain increases as the ring gets smaller:
Chemical drawing programs will tend to keep the general shape of a cyclic structure (a heptagon in the case of molecule f) and just add the triple bond, but it does do a good job of indicating to us that the molecule will suffer from this strain as it naturally tends to deviate the angles away from $180^o$!
Triple bond in carbon means that the carbon atom is sp hybridized. sp hybridized carbon has the two bonded groups at 180 to each other. Therefore it is displayed linearly which is closest to the actual structure. Single and double bonds are at an angle of nearly 109.5 and 120 degree therefore are not drawn linearly.