Is there a way to load DOS games into high memory?
Yes, if you mean the range of 640KB to 1MB (aka adapter space, adapter's segment, Upper Memory Area/UMA).
Problem is, the term for that region varried. Both in time and space (country).
Originally, in English countries, that space was called "high memory". This was in the mid-1980s or so,
when people tried to make their old PCs make use of more system memory for DOS (conventional memory rather than UMBs).
At the time, with Hercules and CGA cards, it was possible to have 704 to 736KB (and beyond with other gfx hardware) of ordinary DOS memory,
provided the motherboard was configured that way..
Later, after XMS came out and Himem.sys was able to use 64KiB (-16bytes) above 1024KB -on ATs- to swap out DOS kernal,
it became "upper memory" (with free memory blocks called UMBs; Upper Memory Blocks).
In German speaking countries, for example, this was not adapted until the release of DOS 7 for several reasons.
In DOS 6.22, the Upper Memory Area (UMA) is erroneously called "Hoher Speicherbereich" (high memory location),
and the HMA (High Memory Area) is called "Oberer Speicherbereich" (upper memory location),
causing confusion with English speaking folks sometimes. Especially when they're around on English forums. 😉