There's probably an easier way to do this, but this is all I could come up with. If your game dates are in A3:A12 (including future dates), try this for your column B team:
=IF(COUNTIF(B$3:B$12,B$3)=COUNTA(B$3:B$12),COUNTA(B$3:B$12),MAX((B$3:B$12<>"")*ROW(B$3:B$12))-MAX((B$3:B$12<>INDEX(B$3:B$12,MATCH("*",B$3:B$12,-1)))*(B$3:B$12<>"")*ROW(B$3:B$12)))&" "&LOOKUP(INDEX(B$3:B$12,MATCH("*",B$3:B$12,-1)),{"D","L","W"},{"Draws","Losses","Wins"})
That's an array formula, so, after typing or copying the formula into the cell, pressCtrl+Shift+Enter rather than just the Enter key. If you successfully enter it as an array formula, it show curly braces surrounding the formula in the formula bar. You can copy that formula across the columns to get the streaks for the rest of the teams. You'll need to adjust the ranges to reflect your actual sheet layout, of course; e.g. if your dates are in A2:A30, change all the range addresses from B$3:B$12 to B$2:B$30 and that one B$3 at the beginning of the formula to B$2.