This is not love for your team, it's simply foolishness. Gambling is actually a game of fun but there's no any form of fun in deliberately losing your money even when you know your favorite team will lose. You can not just be wasting money deliberately and claim it love for your team. You can support your favorite team by sticking with them even during struggling time i.e losing streak, buying their jersey, buying ticket to watch their games and some other ways possible to support them. For the love I have for my team, I don't always gamble on their games unless the ones I am so confident they will win and if they eventually lose, I do feel the pain.
I understand with your point, you're correct supporting a team is when you give an impact to the team. If you gamble, either you lose or win, there's no impact to the team. If you lose, you're actually contributing to the casino, if you win, it's a personal reward.
One of the example is Socios who own Barcelona, they're supporting the team in financial, effort and time.