Technically WINE provides more than just Win32 APIs, but essentially you're right. WINE is more a compatibility layer / wrapper for PEs than an emulator.
In fact, I often make the container distinction: you have containers (Zones / Jails / OpenVZ) and you have virtual machines (VMWare / Vbox / Qemu / etc). WINE falls more into the containers category because it runs Windows PE natively on the host but in a sandboxed environment (and in an approximate sense of the term, chrooted) but with hooks that go between the host and client.
But, like with WINE, many lump containers into the virtualisation pigeon-hole as the full hardware emulation suites even though you're not actually emulating any hardware with containers.
Which is all Wine provides, hence the name: Wine Is Not an Emulator.
(Alternately, I guess you could insist that glibc is a POSIX emulator on top of the OS kernel.)
(My point? All of a sudden I need a point? When did that happen?)