First: your link is broken
But this has been reported a lot over the past few months, its just a matter of time before its fixed
Homie out here cooking some breakfast in the attic
As of now, there is no way to sort the IL page sadly. For some of us, we even get 504 errors when attempting to load the IL page due to the amount of runs present on the profile. It would be nice in the future to have a fix for this. I personally don't see it as a top issue, but a minor inconvenience that can be put off while more major fixes happen.
If the in-game timer is not used in the run, that often means that the timer can be manipulated in some way that creates an inaccuracy in full game runs (which can include excessive pauses), or, there is gameplay at some point during the run that is not tracked with the timer. I would suggest consulting with the game's moderators to find out the specific reasons for not tracking igt.
There have been multiple game requests and forum posts for this game before, and every time it's been rejected, its due to having no definitive ending. You can always try requesting this game, but don't get your hopes too high. Your best bet is to be very specific in the additional notes section, including every category as well as the specific rules for said categories.
I agree with @Kkntucara , the ILS should be separated by biome, not by individual checkpoints. Separating by individual checkpoint is just a massive headache waiting to happen, just look at car obby for an example.
On screen timers and livestreaming is not required. You may screen record your run, upload it to a video sharing platform of your choice, and submit that to the correct category on the board. Personally, I would just use an external device for timing, such as a stopwatch on your PC or watch, and use that for timing. There isn't a great floating timer for iOS at the moment.