Presuming that this was a WX cancellation, UA had no reason to offer to pay for a hotel or to offer a voucher, but the fact is that it did and then confirmed in writing (at least half). UA ought to honor the commitment even if someone hit the wrong key.
I would send in a short letter enclosing a copy of the UA letter and noting that no check was enclosed.
A supervisor reviewing this is likely to simply pay up. But, if the voucher is worth it because you've got other travelers, why not take that?