I think it's good that you're trying to figure out *why* this bothers you.
I had a roughly similar experience with my DH when we first started dating and so I'll ask you a few questions and then tell you my story.
-If you thought your BF would go participate in this sport in the future but would never ever run into Ex again, would you feel more at ease? So, is the issue not necessarily what transpired - that they competed against each other - but more that it might happen again and again and again?
-Are you worried that she still has feelings for him and might try to use this to get him back?
-Are you worried that he might fall for that?
Before we were dating, my DH and his exgirlfriend broke up for various reasons, but one was that she was cheating on him. Based on what he's told me, she did it to get back at him because he wouldn't marry her. So, she wanted him, he wasn't as interested in her as she was in him, and so she handled it by being mean and unfaithful. They broke up and parted ways.
My DH has worked on cars a lot and rebuilt one of his by himself, so he is an expert on this brand of car.
Fast forward a few months. He and I were dating. We were on the phone and he told me "Oh, exgirlfriend stopped by today because she wanted to ask a favor of me." She had bought a used car, of the brand that DH knows a lot about, and she wanted him to look at the engine and inspect it and make sure that it was a reliable car. So he did.
I was pretty angry, but didn't say anything other than "oh." I mulled it over for a few hours. Later, I told him that the situation upset me and he couldn't understand why. I 100% trusted him. I was not worried that he was interested in her. But I was mad because:
1) She had hurt him in the past
2) She had the gall to come and ask him for a favor, after having hurt him so deeply
3) He was naive/nice enough to acquiesce and help her
I knew she was still interested in him. I felt that he was inadvertently leading her on. He was not interested, but by not saying "Back off" he was giving her a green light to continue. And I was afraid she was going to keep showing up and showing up asking for favor after favor, using the "but we're friends now" and "I just need help" routines. I didn't want to be in a threesome where I'm dating him, but he's often interrupting something we're doing together to go help her or do her a favor.
I felt like he just wasn't ripping off the band-aid. He was trying to be "nice" but it was "nice" to her, and not to our future relationship. Time and energy that he could be putting into our relationship, he would be using to continue to do her favors. That is, if she kept coming back for more and more favors.
I told him she should go to the other man, the one she'd been cheating on my DH with, and ask him to look over her car. Or to pay a mechanic. No need to ask my DH for favors.
I said all of this calmly. And I didn't ask him never to see her again. I just warned him that, in her mind, he was leading her on, and that if he kept saying yes to the favors, she would keep asking for them.
She did try several more times, but because I'd warned him that she'd "need his help" again, he was on to her and told her no the next couple of times until she stopped.