This is a font issue. The font(s) being used do(es) not contain a glyph for the character, hence the rendering software displays a generic symbol like a rectangle instead.
If you follow the link Fonts that support U+1F6B6 on the page you mention in the question, you will get the information that only Symbola contains the character PEDESTRIAN (U+1F6B6). (The LastResort font mentioned there is a pseudo-font, useful in software development but not in rendering characters.) This should not be a surprise, as it was introduced in Unicode 6, in 2010. It generally takes about ten years or more for a character to get reasonably well supported in fonts.
Sufficiently new versions of Segoe UI Symbol also contain U+1F6B6, but Segoe UI Symbol is proprietary, shipped with Windows 7 and Windows 8, and you may need an update to it to get a version that supports U+1F6B6. Symbola, on the other hand, is a free font.