My 20 mo old plays by himself, with his siblings (5 mo old, 4 yrs, 6 yrs & 8 yrs old) and sometimes with mom & dad. He does like to scribble, mess with blocks - more knock them down, unfold the clothing, play in the bathroom (which we are trying to brake him of without making the bathroom a "bad" place) push & ride cars around the house. dance with Elmo or when music is on the TV or computer. But he also likes to "help" us with things... like taking the folded clothes to the dressers if he see mom do it, clean up the rooms or yard if he see us do it, put dirty cloths in the washer if mom is, get the recycle ready to go out if he sees if mom is, ect.
Although I am busy with a family of 7 (5 kids at home, hubby & myself... our 8th is away from home) - I do try to make a little time for each of them, if not for play, at least something we do together - reading, baking, cooking or cuddling and watching a show and we also do a lot as a family also - swimming pool, watching movies at home, walks in the Metroparks. playgrounds & McDonald's playground & food as a treat for good behavior.
To answer your question - no you shouldn't have to entertain all day, but you should try to do something with them everyday. And yes playing with clothing and washcloths is normal... or at least in my house it is - even the 8 yr old still does in her own way.