Protein is needed to build muscles, grow, maintain the body, repair the body and make new tissuees of all types.
Horses eat grasses and grains which contain plant proteins.

Protein is found in all plants, but more in grains and legumes and seeds, and nuts.

There are tow types of protein in nature. Animal protein (meat, milk,eggs) and plant protein ( all plants, legumes,serials ..) Carnivores obtain their protein from eating pure meat. Omnivores derive their protein by consuming meat plants. Herbivores by eating plants.

Grazed horses get 90% of their protein from the grass they eat.
The rest of it comes in the form of the grain their diet is supplemented with.
If they are not primarily grass fed – they get most from hay (and different types/quality of hay have different protein contents.. for instance I think Alfafa is the highest protein content hay you typically can get) and the rest fed through Grain/Feed.

You can also purchase additional supplements that contain protein (like Fat Cat) for performance bred horses who need additional protein because of the amount of work they do.

There is protein in everything. Most of the large mammals in the world never eat meat. You wouldn’t call a gorilla a herbivore to it’s face.

Proteins are made from amino acids. When you eat vegetables, your body breaks down the protein into amino acids and then uses them to build a new protein.

The grass is fermented by bacteria in their complex to produce a range of proteins and these plus the proteins in plants they eat are broken down to amino acids which are then use by the animal to make proteins (muscle, enyzes, bones, cells etc)

Muscles use protein as building blocks. Other forms of food can be converted to protein and then to muscle as well. However, that is more inefficient. You would have to eat like a horse to be as healthy.

they get it from plants but they have a different stomach system from us and we cant reproduce it

What makes you think protein is only found in meat? It isn’t.