If the speedo doesn’t work then yes it’s illegal. Is that an intercooler? Some places may have an issue with it sticking out.
If the car is considered an antique you can get away with a lot. People are importing rare 90s Japanese cars because you can get away with having left hand drive. Over 25 years old is considered antique.
No one inspects your car like in Germany they just test emissions. The cops will have to see you and pull you over.
Other than the tires extending past the fender, I don't see anything potentially illegal. The wooden "spoiler" doesn't look properly well attached, but you probably wouldn't be pulled over for that.
Cars in far worse shape than that are driven on the roads here all the time.
In the US each state sets their own requirements for what is street legal. Each state also determines their own vehicle inspection requirements which vary from none to annual.
Then again, this car is in Malibu, California, a general region where you get a ticket for failing to display a front license plate, on a vehicle that has a front license plate.
edit: I just noticed the multi-meter glued to the "dash". Nice.