LICENCE file is a convention, but not an obligation, except for some licences which require you to add the licence to the distribution of the project, e.g., the GPL.
Then some projects include a "this is licenced under X, the licence can be found in the LICENCE" header in each file, others imply that it is clear that all files are licenced under the provided licence.
With the BSDL, some author may have forked the BSDL project, but does not intent to licence it under BSDL again. As long as he did not add anything, you're covered by the BSDL. When he added something, his changes might be proprietary.
What does the BSDL require for licencing?
BSD 2-Clause License
Copyright (c) [year], [fullname] All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the
So it requires you to retain a copyright notice and disclaimer, but not the BSDL itself.
The package.json licence field is intended to display the licence on sites hosting the package, so you can assume that the author wants mark the package to be licenced under BSDL, when he added the line himself.
Finally there is the option to ask him to clarify the licencing, because others may have the same doubts as you.