Is this a correct translation? it doesn't make sense to me.
What doesn't make sense to you? The English sentence, the German sentence, or the translation (meaning bad translation from one to the other)?
the english sentence doesn't make sense. Do they mean written to us?
Yes. The "to" part isn't always necessary. "He wrote us a letter", "we write home every day", "Mom will write Dad a thank you note" can all be used without the "to".
ok I can see how 'uns" in dative case means to us but the english will always require "to us". Their translation is not correct english.
The English does not require "to us". There is an example here in the definitions and examples tab that is similar:
"Write her soon, please."
The "to" is not necessary.
maybe that is American usage.