Is there a context in which this sentence could make sense? :D
A fairy tale?
Maybe a monk who took a vow of silence?
Why not Every year, he should only say one word?
That is měl, not směl.
this "could" is in the sense of "was allowed"? Or "was able to"?
It is in the sense of "was allowed". "Was able to" would be "mohl"
Could we say, "each year he was permitted to say only one word"
Yeah, I think allowed and permitted are basically the same so I will add it.