These are two different ways. We should test both ways: seeking and playing. 
Specifically speaking you're right, you are testing "Video component stores position correctly when page is reloaded" scenario and you're doing it right.
Also you will wait 10 seconds in this test for video to get to 10 seconds position. Using seek() will speed up this.
Also original test was flaky due to seek(). So I would like you to use seek here also. Does it make sense?