Is the Type 1 or PostScript font format dead?

Depends on what you mean by "dead."

The successor to PostScript, OpenType , is simply a wrapper for either Postscript or TrueType outlines, so chances are your new OpenType fonts use PostScript outlines to define glyph shapes.

As far as the format goes, Adobe, the creator of PostScript fonts, has not released any PostScript fonts in years, opting instead to release their font collections in OpenType, which is a cross platform format.

PostScript fonts will continue to be supported for some time to come. The format is not dead, but it could be said it is dying.