True, being a man down can change the game no matter if it was a defender, midfielder, or striker that got sent off. Your opponent immediately gets an advantage, very few teams finish a game with 3 points after picking a red card. Anyone who thinks a striker being sent off doesn’t affect the results of the game is either being sarcastic or is genuinely ignorant.
Most football lovers who actually watch and follow up with football games will agree with this, when a player is sent off from a team, sometimes it doesn't really matter their position, provided its a team member, it gets to tell on the psychology of the team, which in turn can affect their performance in that game. In most cases, these teams results to becoming more defensive so they will not concede more goals since they are not of equal number to their opponent, but then in rare cases, some teams build strength from such, and even end up becoming more aggressive and possibly taking the lead against their opponent. Some team becomes even tougher when they have a man down than they were when they were complete, probably they get that mental awareness that they have a man down and every mistake will cost them a lot.
Anyways, it varies, either of the cases I just cited could play out, its not actually binding it must be one of them, it all depends on the team giving the card and the opponent, and the teams strength and depth too does have a part to play in all of this sometimes.