On the BBC Micro, the operating system has the explicit concept of "language ROMs", of which BASIC was the most obvious example. Other "language ROMs" available included word processors and other business software, as well as other programming languages. Some parts of the memory map were explicitly reserved "for the active language", while others could be allocated dynamically, and still others were reserved to support operating system functions. It was a very sophisticated system for an 8-bit micro.
Typically, the area from &1900 (PAGE) to &7C00 (HIMEM) exclusive was available to BASIC programs, assuming a machine with floppy drives fitted and in the most frugal display mode. Switching to the tape filing system allowed reducing PAGE to &E00; selecting a graphics display mode would however reduce HIMEM automatically, perhaps as low as &3000.
On the 6502, zero-page memory is also important; normally &70-&8F was available to user assembly code without affecting BASIC or other system functions. This was technically part of the "reserved for language" area, but BASIC guaranteed that it would not use that area, limiting itself to &00-&6F inclusive.
A game requiring a lot of RAM could easily supplant BASIC, and thereby use all of the "reserved for language" space as well as all the RAM that BASIC normally allocated (dynamically) to itself. After the load was complete, the game could also overwrite RAM allocated for the filing system. Such games would need to reinitialise both the filing system and BASIC on exit; most simply didn't provide this function, and expected the user to reset the machine by pressing BREAK.
Obviously these options were not available to a game written in BASIC. But most games that needed a lot of RAM were already written in assembler for speed reasons.
A few later games took advantage of the expanded capabilities of the BBC Master or even the Master Turbo - but these machines didn't appear until 1986. On the Master Turbo, the game itself would run in the Second Processor with 62KB RAM available, and also load part of itself into the "host" which was the Master itself. The best known of the games which could do this was Elite.