Yeah Brighton has nothing to lose so yeah it wouldn't hurt that much as Spurs if they loss their match. Spurs are a heavy counter attacking side and right now both their wing backs are getting active into counters as well unlike Arsenal. Kane also is doing some crazy assists so lot of work for Brighton to handle but a draw would be enough to surprise Spurs.
Tottenham will try to play more perfect this to catch up points so as not to fall behind with Arsenal, I know as you said Tottenham have a quick counter-attack they can count on that when Bringhton off guard I think the match could have been interesting and surprised Spurs because they couldn't win.
Still in my prediction, this will definitely be a Tottenham victory, this victory must be passed in order to remain in the top 4 of the EPL.
Of course this will be a tight competition with Arsenal to win the champions league qualification ticket.