I think Lyra was very close in their answer. In fact, I think they actually mentioned the solution phrase within their answer without necessarily realising... The character who is talking here is...
...the second hand on a clock! The running track in question isn't your typical outdoor athletics facility but a clock face, explaining how/why they'd "spent the whole day here, running laps" i.e. moving round the entire clock face (1 lap) every 60 seconds, all day long. 'Everyone [they] passed' implies the minute hand and hour hand, which travel more slowly.
Lyra has identified the relevant context for each of the shouted-out remarks, just not quite pushing the second, third and fourth to their full extent...
"Hey, didn't I see you at Goodwill?"
As mentioned by Lyra, Goodwill is a US nonprofit organisation with thousands of thrift stores (charity shops) where you can buy things second-hand (i.e. used).
"Were you the guy from the start of the poker game last night?"
The 'second hand' is the round ('hand') immediately following the opening round in a poker game, i.e. which occurs very near the start of the game.
"Can you stop it with the applause all the time? I needed to go straight home after the show, but the actors kept coming out to bow because of your ruckus!"
To give someone 'a big hand' means to applaud (like at the end of a theatre performance), so giving a performer a 'second hand' might suggest you are applauding them repeatedly.
"Thanks for replacing the bosun when he got sick! I know it's your job, but I still wanted to tell you that you did really well"
A 'hand' is also a crewmate on a ship, so a 'second hand' (in the vein of a 'first/second mate' or 'first/second officer') might be someone who deputises for a more senior crewmate when required.
As for the question of whether this character will 'qualify for the Olympic 400m dash at this rate', here are two possible interpretations...
1. If it takes this character 60 seconds to perform 'a lap of their circuit' (i.e. to go around the clock face), this doesn't put them anywhere close to a professional 400m runner's lap-time on their track. At the Tokyo Summer Olympics in 2021, the slowest female runner in the heats clocked a time of 55.89 seconds and the slowest male 48.53 seconds. With this comparison the 60-second lap time of the second hand means they are very unlikely to qualify.
2. If instead we are merely to make deductions based on their name, then perhaps they might qualify but they are unlikely to win - after all, they will always be 'second'!