I believe the file you linked to is the correct one – the list of symbols which will be parsed as infix multiplication (like *) is long, but doesn’t include ★. I don’t know of a good reason for that, it could be just an oversight?
* / ÷ % & ⋅ ∘ × \ ∩ ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊓ ∗ ∙ ∤ ⅋ ≀ ⊼ ⋄ ⋆ ⋇ ⋉ ⋊ ⋋ ⋌ ⋏ ⋒ ⟑ ⦸ ⦼ ⦾ ⦿ ⧶ ⧷ ⨇ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨻ ⨼ ⨽ ⩀ ⩃ ⩄ ⩋ ⩍ ⩎ ⩑ ⩓ ⩕ ⩘ ⩚ ⩜ ⩞ ⩟ ⩠ ⫛ ⊍ ▷ ⨝ ⟕ ⟖ ⟗
Note that it does include ⋆, there’s a chance these were judged to be too similar? Both are things you can type:
help?> ★
"★" can be typed by \bigstar<tab>
help?> ⋆
"⋆" can be typed by \star<tab>