We have seen many videos by now that Muslims are praying in the streets. By the masses. In every big city of the world.

Why would they do that, as they have their mosques?

Are they allowed to this this by Islamic law?

Let's see:
https://www.sistani.org/english/book/48/2226/

(MAKRŪH) Ruling 884. Performing prayers is disapproved in a number of places, including:
1. a public bath;
2. on saliferous land;
3. facing a person;
4. facing an open door;
5. on a street, road, and in an alley, in the event that it does not cause trouble for passers-by; if it does cause them trouble, it is unlawful;
6. facing a fire or lamp;
7. in a kitchen and in every place where there is a furnace;
8. facing a pit or ditch where people urinate;
9. facing a picture or statue of a living thing, unless it is covered;
10. in a room where a junub[1] is present;
11. in a place where there is a picture [of a living thing], even if it is not facing the person performing prayers;
Etc

These people are acting against their own laws!!