Without further context it would be hard to answer, because there are several variants of -test (one sample, for independent samples with equal, or unequal variance, for dependent samples, etc.). Nonetheless, statistic and degrees of freedom are defined in terms of things like mean, standard deviation, and number of samples for both groups, where the formulas for calculating them can be found in statistics handbooks, and many places on web, including Wikipedia. I'd recommend you find the appropriate variant of the -test that you are using (are you sure that the spreadsheet calculates the correct one for you?) in Wikipedia's article and calculate it by hand, you need nothing more then the pocket calculator for this.

TTEST Type

In your TTEST formulas you are specifying a type of 1 which is a 'Paired Test'. The 'Paired Test' requires an equal number of data points to be compared. If you change the type to either of 2 or 3 you would no longer get the array mismatch #N/A error.

Formula

=TTEST(range1, range2, tails, type)

1. One Team's Results vs. All Teams'
   This seemed to be what you were attempting in your formula

=TTEST(FILTER(score, team=F8),
       score,
       2, 2)

#  If excluding individual team from all 
#  teams' results then amend as follows

=TTEST(FILTER(score, team=F8),
       FILTER(score, team<>F8),
       2, 2)

2. Games 1-3 vs. Average Games 1-3
   ^{Uses array of AVERAGE Games 1, AVERAGE Games 2, & AVERAGE Games 3.}

=TTEST(FILTER(score,team=F8), 
       { AVERAGE(FILTER(score, game=1)),
         AVERAGE(FILTER(score, game=2)),
         AVERAGE(FILTER(score, game=3)) },
       2,2)

#  If excluding individual team from all 
#  teams' results then amend as follows

=TTEST(FILTER(score, team=F8), 
       { AVERAGE(FILTER(score, game=1, team<>F8)),
         AVERAGE(FILTER(score, game=2, team<>F8)), 
         AVERAGE(FILTER(score, game=3, team<>F8)) },
       2,2)