@JanKor,
NYT's Connections, Strands, daily Mini crossword: I like them and they're paid for in my all digital access bundle.
Both Gothamist's and WBUR's mini crossword. It's free and I get an email reminder.
Neither technically daily nor word games:
Weekly news trivia quizzes from NPR, WBUR/Boston.com, and NYT. There's the history trivia game, Flashbacks from NYT.