minecraft testfor @r[r=13] "/gamemode "that player" adventure" [closed]

Short answer: No.

Slightly longer answer: testfor doesn't work this way, it only performs at test, and can't do anything with the result. Don't use testfor for anything other than debugging! (Or at all, since it was removed from the Java edition in version 1.13.)

But to actually answer you question, all you need to do to set a random player to adventure within a radius of 13 blocks is the following:

/gamemode adventure @r[r=13]

for Java edition versions 1.9 (1.8?) through 1.12 (and I believe this applies to Bedrock edition) or

/gamemode adventure @r[distance=..13]

for Java edition versions 1.13 and above.