I think a hard and fast “yes or no” to this question is the wrong answer. If you limit yourself to yes or no then the answer is an objective, yes. Yes, the game is built to be played by a team of players who use a team of characters to collaboratively achieve their goals.
There are plenty of rules in D&D 5E that support team play. In fact, there are thousands of examples. A lot of those rules are situated in the character builds section, not necessarily the core rules. For example, one of the 5E barbarian rage options provides all allies advantage on attacks to a target if the barbarian is adjacent to the target. The barbarian gets nothing from that ability. Only his allies benefit for it, making it an option that supports team play. D&D 5E is littered with options like this that support the team. They may not be situated inside the core rules, like the Aid ability, but they are there and should not be overlooked.
That said, I think some of you are tripping yourselves up when you compare D&D to other games (using the Savage Worlds example) and saying, “Well, that has more obvious rules elements that support a team dynamic. So that is a team game and this is not.” I think you’ve accidentally mentally cut yourself off at the knees so let me give you some things to consider.
The answer to the question should not be a hard yes or no. The more interesting consideration is “To what degree is a D&D built for team play?” Because from a game design perspective, there is a spectrum of options that support team play. So just because Savage Worlds is more oriented towards team play doesn’t mean D&D is not oriented towards team play. It’s just oriented in that direction to a lesser degree.
What you should look at is a spectrum from “solo game” to “100% team-oriented play”. D&D can be played solo but I think it works better when a group is playing and supporting each other, making use of those options. When comparing two games, I agree Savage Worlds is definitely closer to 100% team-oriented play end of the spectrum than D&D is but that doesn’t mean D&D isn’t a game about team play at all.