Just tested it on two more machines including a my gaming rig with 12gb ram and still it crashes pretty much every time .

*Update*

Seems like if after selecting the two runes you set the filter back "All" the client doesn't crash

if you could post the logs from one of the sessions you crashed in that would be helpful. The logs are located here:
C:\Riot Games\League of Legends\air\logs

you may have to zip it in order to attach it.

I have the same problem. I had 3 different cases of crashing so far:
1.) Click combine, the two runes merge together and the middle glows. crash.
2.) Click combine, it merges and shows the rune, it moves over. crash.
3.) Clicking Get Runes, going back to the rune screen -> "waiting for server" (or something like that, i don't remember it exactly :/) -> crash.

Here are the logs from all three crashes:
*Click me*

Todays Logs (2 archives due to file size limit) -

I can additionally vouch for this recurring crash.

PS: It seems to only do it if you organize the list. When the runes are all set out and I go to combine, it works just fine.