You are of course right about 「～たり（～たり）する」being used in its multiple ～たり form to list several possible actions, but it does not HAVE to list multiple possible actions in order to be used to represent more than one action.
When only a single action is mentioned, there are two ways to look at it. Either there is another unmentioned action that might happen, or there is more than one possible object of the single action mentioned.
It's pretty clear that the person is saying that on the weekends they play at Round One. Either they also do other things beside play on the weekend, or else they also play elsewhere besides at Round One. Because this ～たりする form is so open-ended, either way you want to think about it is valid, until context provides more clues.
So going back to your example
...In this case, since it seems unlikely that the speaker would do some other action than "think", he must mean that he also thinks OTHER things, besides the thought that he chose to mention.
therefor I would translate this as:
People will get used to any kind of environment... I sometimes think.
The reason I choose to use the word "sometimes" is that it is the best English choice to represent the idea that it is only ONE of the things this person might think, thus preserving the sense of ～たりする.