question: white to move, in this game, can white move and check the king?
Royal Shield: "Matrimonial Chess"

That rule is the same as normal Chess. You can't move in to check, even if it means check or mate to your opponent.

I found something simmilar. https://greenchess.net/rules.php?v=coregal
Royal Shield: Matrimonial Chess
“In Royal Shield: Matrimonial Chess, the King lives as long as his Queen reigns!”
Hi everyone,
I’d like to share a custom variant idea called Royal Shield: Matrimonial Chess. It keeps the feel of standard chess but adds a dramatic twist:
Core Rule
The king cannot be captured or checkmated as long as at least one queen remains on that player’s side.
Checks still apply. The king can be put in check, but while in check, all of that player’s queens are frozen until the king escapes.
Pawn promotion: Promoting to a queen restores the Royal Shield if all queens were previously lost.
Why It’s Fun
Protecting your queen(s) becomes critical—you can’t win until every enemy queen is gone.
Checks become a weapon to paralyze the opponent’s queen(s) rather than rushing for mate.
Late-game pawn promotions can swing a lost position back to safety.
Example
A player down material but with a single queen survives a normal mating attack. The opponent must first capture the queen while using checks to freeze it, creating a completely new layer of strategy.
I’d love feedback from players and staff—does this sound like a variant you’d enjoy?
Thanks for reading,
Kevedes