It is true that the variations in field strength propagate radially from the transmitter.
However, as your diagram shows, the fields themselves are vector fields, and the orientation of the vectors (both electric and magnetic) is at right angles to the direction of propagation. They have no effect on a conductor oriented radially.
In a comment, you mention:
Now, I'm thinking about the receiving antenna as a wave guide.
Yes, that's a good analogy. In fact, that's the principle behind the Beverage antenna alluded to by hotpaw2. It works only because it is physically close to the ground, which makes it part of a transmission line — a kind of wave guide. The propagating E field induces a voltage between the wire and the ground. This wave of voltage moves along the wire at roughly the same speed as the radio wave, reinforcing signals coming from the correct direction. Signals arriving from other angles interfere with themselves destructively.