It looks fine in my browser (although right after the page loads I see exactly what you describe, only after a while it displays properly).
Anyway, here is the code:
iconGraphics = Graphics @ Text @ Style[#, FontFamily -> "Chess Alpha", FontSize -> 34] &
/@ {"k", "q", "b", "r", "h", "p", "l", "w", "n", "t", "j", "o"};
icons = AssociationThread[{"K", "Q", "B", "R", "N", "P", "k", "q",
"b", "r", "n", "p"}, iconGraphics];
ImportString["5n2/3nrpk1/1qBp2p1/p2P3p/1rp1PP2/2N4P/1P2RQP1/4R2K w - - 4 69", "FEN",
"Icons" -> icons]