The feeling I get from your translation is that it is technically correct but not very idiomatic for the first half.
Unfortunately I can't really put a finger on what it means for the first part of the sentence, but I'll give a suggestion below for you to compare to.
I purposely chose something different to give you new ideas.
The structure of the second half is unclear to me.
I read it thus:
Si contenderis ut perdas peior quam omnino non contendere sit.
If you race so that you lose is worse than to not race at all.
Distilling to the core structure, this seems to become:
Si contenderis peior sit quam contendere.
If you race it is worse than to race.
(This might sound logically silly, but that's irrelevant. Focus on syntax now.)
I don't think a conditional clause can function as a subject.
The subject of the main verb sit should rather be a noun, a pronoun, or an infinitive.
Moreover, if the subject is something like an infinitive, it is treated as a neuter and the adjective should be peius instead.
To fix this core structure, just use an infinitive for the subject:
Contendere peius sit quam contendere.
To race is worse than to race.
Then for the subordinate clause.
You can have a clause subordinate to an infinitive, so that's no issue.
To me it seems that you have a final clause ut perdas, "so that you lose" or "for the purpose that you lose".
The final ut clause expresses a goal, not a result.
I think this would work better with two infinitives like in English.
If you want to say "to race so that you lose" without infinitives (and without the final clause which means something else), you could make use of gerunds or participles.
This leads to options like contendere et perdere, contendere perdens/perdendo, and perdere contendens/contendendo.
I would take a somewhat different approach.
First, to say that some action is characteristic of someone, you can say hominum est currere or similar.
I would consider using something like this for an idiomatic way to phrase the first part.
And even if you have a noun instead of an infinitive, I feel that a genitive is better for expressing a characteristic than a dative but both work.
(I'd be happy to hear whether others agree with this view.)
Then we need suitable words.
Circus is a good word for a race track.
For racing or sport I would use certamen here.
Latin likes adjectives when adding details, so I think certamen circense is an idiomatic way to say "chariot-racing".
I'd leave the word "sport" out completely, as I don't think ludus or any other added word would add much clarity.
While rudis is certainly possible, I find myself considering tiro somehow more idiomatic.
With these ingredients, I'd put the first half like so:
Certamen circense haud tironum est.
Chariot-racing is not a sport for amateurs.
To me certare sounds more like a competition against others, whereas contendere more like a time trial, where you are trying to make the course as fast as you can.
You are not just stretching for the goal in the message you want to convey (context matters!), but fighting others for the first place.
But do bear in mind that I may have gotten some of the nuances wrong.
For the second part I would use infinitives, putting the structure close to the English original.
I'd also make the statement unreal, so as to underline the impossibility of losing.
Of course there is a chance to lose, but we're talking about confidence in invincibility.
Certare et perdere peius esset quam non certare!
And to compete and to lose would be worse than not to compete at all!
Or if this feels like too many infinitives and you don't want certare twice, you could go:
Perdere certans peius esset quam non certare!
And to lose when competing would be worse than not to compete at all!
Another aspect that I like with this whole is that certamen and two certares frame and structure the whole thing.
My final and complete suggestion is therefore:
Certamen circense haud tironum est. Perdere certans peius esset quam non certare!
