I've never seen live betting be for the remainder of the match, on any site (or live sportsbook) in over a decade of gambling.  It's always been a line/odds for the entire match.  The reason for this is that there is no base of reference.  It's hard to reconstruct what the exact score was 2 minutes 43 seconds into the game or 11 minutes 17 seconds into the game.  The only bet I've ever seen that's for the remainder of a match is a halftime bet.