SC2 has 3 very distinct races (he gives it a 8.8 for variety), hence there are just 6 possible matchups. AoE 2 (DE) has 35 (he gives it a 3), making over 600 possible 1v1 matchups. This creates a huge amount of extra work to ensure matchups are enjoyable - yet (at 1650+ Elo) there are just 2 races with > 55% winrate (Franks @ 56.98% & Celts @ 54.21% on random map). Despite the good balancing, tournaments also come up with rules to limit the impact of the best civs, normally with specific civ bans and limited picks in a series. It's really only because of the huge overlapping tech & unit tree that this is possible - if there were more diversity there would be too many variables to balance around. This is further compounded by the variety of maps which the game is played on - as he does mention the map does affect which of these are viable, and this makes the game even more interesting and diverse since you need to adjust to multiple types of map. SC2 on the other hand has a much smaller responsibility in this regard: provided there are interesting viable builds within each race the task to balance across-races is minimal. SC2 also only has 7 maps in the pool (at least, right now) and just spawn positions are randomized. This makes preparation way more important, and less dynamic.
Both AoE and SC2 also use the space as a stop-gap for specific strategies - it's a way for the less aggressive player to fend off early aggression, but also a way for a more dominant player to choke out resources. Traditionally this is done by controlling the entry to your main base or your expansion (in SC2), but in AoE it's way more open and difficult to accomplish this most of the time. This importantly makes players rely on very adhoc dynamic walling, often incorporating undestroyable natural resources (like gold deposits).