sounds like a blitz variant for chess.com ... 
p.s. I've heard this called "King in hand" rule. Example: before a blitz game, one may ask if they play with "King in hand"? To which "yes" would allow the King to be captured.
OTB capture exposed king
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In OTB chess five minutes games or less if you expose the king your opponent can capture and win the match.
Chess sites should be made that way. That would be awesome.