No, this is nothing like a real gacha game at all. Gacha games have a wide variety of mechanics, and can have significant depth to them. Trading card games were the original gacha games, and those have entire competitive scenes with tournaments, etc. (Magic the Gathering, Yugioh, Pokemon TCG). Digital gacha games are similar. In a real gacha game you aren't rolling for a static number, you're rolling for a package of numbers and modifiers and mechanics that feed into a complicated combat system, and there's tons of strategizing around how you combine different packages of numbers together in deckbuilding/teambuilding, plus the decision-making in the battles themselves.
Gacha is really just a monetization approach. The mechanics that accompany it are the real draw, and you can have card games, RPGs, tactics games, action games, etc.
You have all that with Gacha pulls and battle system.
The battle system is too rudimentary to capture the essence of gacha. Insofar as gacha lends itself to gameplay mechanics and not just monetization, deck/teambuilding is absolutely integral. Obviously, the game is a parody, but even as a parody I think it does a poor job of capturing that aspect of building and experimenting with your deck/team. Which is fine, not a criticism of a silly little app, but the person I was responding to asked if this is what real gacha games play like and why people play them and I do not believe this is sufficiently representative.
In fact, I would describe this as an idle game, not a gacha game. In other words, a gacha-themed Cookie Clicker reskin. The emphasis is on the gacha, but in a real gacha game, rolling gacha occupies <1% of the playtime, and this doesn't adequately capture how the gacha model intersects with real gameplay mechanics.