A list of names and times should be enough then? they could include an age category, and a sex category and that should be enough.
If it is a fun run, talk of course records is a bit crass.
I used to do a lot of competitive running, everything from hugely organised half marathons to a local sports club having a 5 or 10k run round the woods. With times and age/sex categories and participation medals etc (it used to be a huge thing in Germany - going to a Volkslauf was a regular sunday activity, especially in the army as the biggest "team" entered often won a barrel of beer.)
The parkruns sound a lot like the Volkslauf thing - so a lot of people are competing against themselves, or the person just in front of them - but there were results and rankings. parkrun doesn't seem to know what it wants to be, what with being inclusive, not competitive and then having lists and records. It really needs to decide if it's flesh or fish or fowl.