I know I'm progressing into the meta a little here. And I almost feel silly bringing this up, because it borders into the absurd.
Anyway, are there any ... I hesitate to call them "games" that require zero components and, preferably, zero opponents?
I suppose these might be called mental games, puzzles, or mind exercises.
If learning a language, you can exercise your vocabulary by naming the objects & saying the numbers (e.g. street numbers) which you see around you in the target language.
Practice your math skills on random numbers you see around you (e.g. on license plates), e.g. computing sums, or finding factors, or rapidly estimating how many of something you see and then counting to see how close your estimate was, etc.
Observation games, e.g. noticing as many instances as possible of some phenomenon (e.g. the bizarrely large number of clothing and accessories which have a US flag).
Mentally sort people you see according to various criteria (height, weight, age, hair length, whatever). Hmm, perhaps reading about autistic behaviors could provide more such ideas of structured puzzles/games/activities.
On a similar but separate note, are the any games you can play "with" other unaware people?
Try to steer a conversation so that the other person says some specific strange word without noticing that you steered them to do so.
Intentionally misuse or mispronounce some common word and see if/how people react. More generally violate some innocuous cultural custom, e.g. physical distance between people when talking, length of continual eye contact, etc.
Pickpocketing them as street magicians do? Sounds dangerous and difficult!
A game with no components that can be played solo...are you just finding a really roundabout way to describe thinking? Thinking is pretty great though
As for games with unaware opponents. I did a lot of improv theatre, sometimes I adopt one of the rules of an improv game, I win if I can carry on the conversation without the other person thinking I'm talking wierd. It's pretty easy with something like the alphabet game (each utterance must start with the next letter of the alphabet) but harder to pass off as natural if you've decided your statements will rhyme with what the other person is saying.
Play too many games with unaware opponents and you'll get a reputation though.
Although not solitaire, games folks play to pass time while traveling come to mind (ie SlugBug, I Spy, etc) and the following may qualify as "games you can play 'with' other unaware people".
My favorite was always Treknotland. It can be played in a car with one person or even a large group. Its a riddle with a group twist. The start player decides the riddle's answer and proceeds by giving hints in the form of a riddle. This is accomplished by naming what is "in" Treknotland and is "not in" Treknotland. Players who think they know the answer must answer back in the same riddle form correctly and consecutively to let the start player know they have solved the riddle without giving it away to any other players. The player that solved the riddle is not excused from play and assists in providing hints to other players in riddle form, not to mention assisting in "authenticating" other players who have solved the riddle.
I crashed a party of 50 from a pick up truck hood in less than 30 minutes with this game.