I think you are correct to wonder why that peak is singlet. The truth is that it depends on the conditions that the spectrum was acquired such as spectrometer frequency, solvent, etc.
Due to the double bond, there is a small $^4$J$_H$$_H$ coupling between the CH3 and olefinic CH2. If you look carefully, you can see in your spectrum that although it says singlet it is actually a triplet due to the tiny shoulders that are barely visible about a bit more than half way on the peak! However, for a weak spectrometer (200-300 MHz) and depending on the solvent and conditions the measurement takes place, it can appear as a slightly broad singlet. Similarly, the olefinic peaks that are stated as doublets are not real doublets but multiplets due to multiple small coulings with the aliphatic CH3 and CH2. They can appear as slightly broad doublets though if resolution is not great or even a broad singlet. You would be able to see all these finer details clearly with a high filed NMR instrument (e.g. 700 MHz) and zooming in the aquired spectrum.