There is a good deal of validity towards calling Wine an emulator in this vein. It is reimplementing an executable format loader, calling conventions, and the entire runtime and libraries of a foreign operating system -- in other words, emulating the Windows operating system.
However, emulating has also often been used to describe software that implements the opcodes of a foreign instruction set in software. For example, a program that implements 6502 opcodes and related modules that allows you to play NES games on a PC. Wine isn't an emulator of this type. Wine relies on the fact that x86 Windows programs can be made to run on x86 Linux by means of implementing everything I stated in the first paragraph. It does not allow for running x86 Windows programs on a SPARC machine (QEMU can assist in doing this, but that's a digression...). Wine is not an ISA emulation, but it is an ABI emulation.
However, emulating has also often been used to describe software that implements the opcodes of a foreign instruction set in software. For example, a program that implements 6502 opcodes and related modules that allows you to play NES games on a PC. Wine isn't an emulator of this type. Wine relies on the fact that x86 Windows programs can be made to run on x86 Linux by means of implementing everything I stated in the first paragraph. It does not allow for running x86 Windows programs on a SPARC machine (QEMU can assist in doing this, but that's a digression...). Wine is not an ISA emulation, but it is an ABI emulation.