its a very safe idea to predrill any manufactured wood products such as ply or MDF. If its higher quality ply the glues and the opposite stranding and wood hardness add resistance, were you hand or using an impact? if its lower quality and youre near an edge it can de-laminate and split.. Cabinet fasteners can vary in grade quite widely. That looks like really high quality ply and cheapish screws..
Most of the time I would pre-drill but currently my smallest drill bit is 3mm and I was too lazy to drive to Screwfix to get some smaller bits. Normally I use half decent quality wood screws and find they drive well into manufactured board (as you say, if not too close to the edge), but these are quite small and made of cheese or some other poor quality metal substitute.
I did expect them to round out a little (despite using good quality Wera screwdrivers), but sheering a head clean off is a first for me.
Thanks @ScapingScotsman! As mentioned above I'm all self taught, so it's definitely doable if you wanted to give it a try yourself.