This is completely false. Both use images for the board and pieces, so you can play just fine.

Both do use icon fonts for some of their additional controls on the right hand side, but they all have tooltips so that you can identify them even without the icons. Chess.com uses a bad icon font that uses non-PUA code points (e.g. V = New Game, , = Move Back, … = Move Forward, g = Show Hint), so those ones will be broken. lichess.org uses PUA code points (except for “½” for “Offer draw”), so I think that those icons would even be loaded if you weren’t like me in just blocking web fonts outright.