It's not just spelling that has deteriorated. There's been a dumbing down of the language just as predicted in George Orwell's famous book, 1984.
'Cinema' and 'theatre' are different words for a reason, but some uneducated cinema owners decided to use the phrase 'movie theatre' to describe their facilities. It was either because they were ignorant or pretentious, but now we're stuck with it. To make matters worse, 'movie theatre' became 'theatre'.
It's become so common that the general public don't recognize the improper use of the word any more. A theatre is a place where live performance takes place. When someone says they are going to the theatre, it suggests that they are attending a play or something of that nature.
Cinema is the correct word, but increasingly, even 'educated' people seem to be using 'theatre' and 'cinema' interchangeably.