using plastic wrap

An alternative to plastic wrap is a simple shower cap. They're relatively cheap, reusable, and can fit all sorts of bowls. Check the nearest beauty supply store where you might find packages  containing 20 or more for less than $3.00.

with a tiny hole drilled in the lid. Any food safe  container with a lid should work fine. 

a plate, or a towel (dry or damp), or a container with a lid (either sealed or left slightly open or with air holes) is about what is available and works the best for you in your environment.  All you are trying to do is keep out any possible contaminants, and maintain the moisture level of the pre-ferment / dough, while allowing enough "breathing space" for the wastes from the yeast to leave the dough.

My kitchen is extremely dry, so I need to seal the moisture in with the dough and so use a heavy plate over the mixing bowl (if I'm just resting it during autolyse or mixing), or keep it in a see-through plastic container with a lid (no holes) when bulk fermenting.  I do a retarded proof in the fridge, and so cover the entire banneton in a sealed plastic bag to keep all of the moisture inside.

If your environment is more humid, then using a dry towel might work well for you, or you might find that a container with the lid not quite seated or with breathing holes is a better option.

Plastic wrap, for most people, is fast and convenient and is considered a good barrier to prevent contamination or cross-over from other foods.  It can be sealed tightly or left loose enough for air to escape (or for dough to increase in volume).  It most certainly is not required, and can be replaced by whatever is easiest and most efficient for you.

I bought a few of those plastic bowl covers. They still do a great job of covering my dough bowls. I use a smaller one for the preferment and one larger one for the dough.

I have been putting my dough in a plastic container with lid in the fridge over night, but I have sent for pack of 20 shower caps to cover for the second rise before baking.

I use disposable plastic shower caps from the dollar store (8 for a dollar) to cover bowls. As long as they don't touch the dough I reuse them. I'll use greased plastic wrap to cover sheet pans full of buns, or bagels, or even shaped loaves, if I'm going to proof them in the fridge. I put the whole pan into a large garbage bag but don't want the bag to touch the loaves (sometimes garbage bags are treated with something to kill germs and/or keep them from smelling bad; don't want this to touch the dough!). Things overnighting in the fridge will get very dry if not covered well. If it's a fairly 'wet' dough and will be proofing for a short period of time at room temperature I'll cover with a dry towel. Makes it easier to score the loaves when ready.

So glad things has already been asked. Baking is the only thing I use plastic garbage bags for and I'd prefer to get away from that! :)

It's just how the author did it.

99% of the time the author's measurements and technique are not something fixed in stone there are almost always  many different ways you can go