I wonder if any hieroglyph-like orthographies use semantic radicals in a way comparable to how Mandarin Chinese does, or if the radical is unique to Chinese and other similar languages?
As pointed out, Egyptian hieroglyphs employed certain symbols as semantic determinants, which though phonologically mute and often redundant would help the reader figure out which concept was intended. There seem to be plenty of available details online about this (Wikipedia, etc.) so I won't go into it.
The other well-known "hieroglyphic" writing system, Maya script, is a mixture of logograms and syllabic characters. Apparently it was mostly the syllabic characters that were used to disambiguate or supplement the logographic (semantic) readings, and not the other way round. There were some semantic determinatives, though (see here, p. 19):
A semantic determinative is a sign that specifies the meaning of certain logograms that have more than one meaning. Semantic determinatives, however, are without phonetic value (cf. Zender 1999: 14). The most oft-cited example of a semantic determinative in the Maya script are the cartouches and pedestals that frame so-called ‘day signs.’
In a comparative work Maya script is said to employ semantic determinatives in a particular way. After citing a trio of near-homophones which are spelled with the same glyphs, it says that
... such spellings would have been ideal for disambiguation by means of a semantic determinative. However, in actuality there is no example where a semantic determinative is used with such spelling. T561.23 CHAN-na could be used to spell any of these three lexemes, and so could T/AC6 CHAN ‘snake’, and T1010/SN4 or IV/004 CHAN ‘four’ (Houston 1984; Lounsbury 1984). As shown below, semantic determinatives had a different function in Mayan; to distinguish between types of orthographic values, such as between a logographic value and a syllabographic value, as with the case of SPHERULEST710/MZS CHOK ‘to throw down’ versus T710/MZR ye, or to distinguish between values of the same logogram with very different phonetic realizations, such as between MOLEPC4 XIB’ ‘male’ versus T1008 WINIK ‘man, person’.
There are not many of these determinatives in Mayan writing (the work cited above says "only a few"), so they're not comparable, I think, to the profusion of semantic radicals found in Mandarin Chinese.