So am I to take it that the interpreted part is a requirement in the language specification, or is it misleading to say that the language is an interpreted programming language when respecting the difference between a language and its many implementations?

EcmaScript language geeks often use the term "ES interpreter" to refer to an implementation of EcmaScript, but the spec does not use that term. The language overview in particular describes the language in interpreter-agnostic terms:

ECMAScript is object-based: basic language and host facilities are provided by objects, and an ECMAScript program is a cluster of communicating objects.

So EcmaScript assumes a "host environment" which is defined as a provider of object definitions including all those that allow I/O or any other links to the outside world, but does not require an interpreter.

The semantics of statements and expressions in the language are defined in terms of completion specification which are trivially implemented in an interpreter, but the specification does not require that.

8.9 The Completion Specification Type The Completion type is used to explain the behaviour of statements ( break , continue , return and throw ) that perform nonlocal transfers of control. Values of the Completion type are triples of the form (type, value, target), where type is one of normal, break, continue, return, or throw, value is any ECMAScript language value or empty, and target is any ECMAScript identifier or empty. The term “abrupt completion” refers to any completion with a type other than normal.

The non-local transfers of control can be converted to arrays of instructions with jumps allowing for native or byte-code compilation.

"EcmaScript Engine" might be a better way to express the same idea.

There are no static compilers for JavaScript apparently

This is not true. The V8 "interpreter" compiles to native code internally, Rhino optionally compiles to Java bytecode internally, and various Mozilla interpreters ({Trace,Spider,Jager}Monkey) use a JIT compiler.

V8:

V8 increases performance by compiling JavaScript to native machine code before executing it, versus executing bytecode or interpreting it.

Rhino:

public final void setOptimizationLevel(int optimizationLevel) Set the current optimization level. The optimization level is expected to be an integer between -1 and 9. Any negative values will be interpreted as -1, and any values greater than 9 will be interpreted as 9. An optimization level of -1 indicates that interpretive mode will always be used. Levels 0 through 9 indicate that class files may be generated. Higher optimization levels trade off compile time performance for runtime performance. The optimizer level can't be set greater than -1 if the optimizer package doesn't exist at run time.

TraceMonkey: