As the old adage goes, "A Picture is Worth a Thousand Words." Perhaps a picture is required. I apologize in advance for any redundancy with explanations provided in the Comments.
There are four functional groups in question. I have arranged them as substituents about a single carbon atom with arbitrarily assigned stereochemistry and atom numbers. A digraph is the best way to assign priorities to the four substituents. Duplicate atoms (ghost, phantom, etc.) are shown in parentheses and they have the same atomic number as their non-duplicate (original) atom. However, duplicate atoms have three atoms of atomic number zero attached to them and they are not displayed in the digraph. Their designation is {0,0,0} and, by default, have the lowest possible ranking.
In sphere 2 (red numbers) all of the carbons are equivalent. No priorities may be assigned. Progressing to sphere 3, one has $\ce{C2}${3,H,H}, $\ce{C4}${5,(4),(4)}, $\ce{C6}${7,8,9} and $\ce{C10}${11,(10),H}. With the atoms in braces ranked in descending order of priority and looking for a first difference, it is clear that $\ce{C2}${3,H,H} is the lowest priority atom with $\ce{C10}${11,(10),H} the next to lowest priority. To distinguish between $\ce{C4}$ and $\ce{C6}$, one must proceed to sphere 4. Here $\ce{C4}$ displays {(5),(5),H} which is higher in priority than that which is offered by $\ce{C7}$, $\ce{C8}$ or $\ce{C9}$--namely--{H,H,H}. Therefore, the priorities of the carbon atoms in sphere 2, and the groups of which they are comprised, have the ranking $\ce{C4}$>$\ce{C6}$>$\ce{C10}$>$\ce{C2}$. In other words, yne>t-but>ene>ane. The compound has the (S)-configuration.