Sorry I missed that the deed was just done in 2021.
I don't see (after only a quick glance) how it can work for your parents. But you should consult a provisional tax advisor (CPA, EA, or attorney) to get specific advice taking into account your situation rather than relying on an Internet form for amounts as large as are involved here.
The general rule is in I.R.C. 121(a), which reads:
(a)Exclusion
Gross income shall not include gain from the sale or exchange of property if, during the 5-year period ending on the date of the sale or exchange, such property has been owned and used by the taxpayer as the taxpayer’s principal residence for periods aggregating 2 years or more.
Unless there is an exception in the rest of section 121, your parents must both have owned and have used the home for 2 years. Otherwise they don't get the $250k/per person exclusion and will have to pay capital gains.
There is some discussion of the ownership tests in the regulations, but I don't think there is anything that helps you. But you and your advisor should review them. See
https://www.law.cornell.edu/cfr/text/26/1.121-1
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