Yes, a total market fund should include small-, mid-, and large-cap equities. In the case of FSKAX, it follows the Dow Jones US Total Market Index, which from your link:
The Dow Jones U.S. Market Index (DWCF) is a total market index that represents the top 95% of the U.S. stock market based on market capitalization.
So by definition the smallest 5% are excluded.
Additionally, it is capitalization-weigthed, meaning it holds more of the larger equities and less of the smaller.
These factors may make FSKAX, in particular, look more like large-cap fund than a total-market fund.
If you read the Objective section of Fidelity's page on FSKAX, you'll see (emphasis mine):
Seeks to provide investment results that correspond to the total return of a broad range of United States stocks.
Compare this to the objective listed for VTSAX:
The investment seeks to track the performance of a benchmark index that measures the investment return of the overall stock market.
So yes, a total-market index fund should include all capitalizations, but whether a particular fund does, or to what extent, will vary between individual funds. If you aren't happy with a particular fund's coverage of the market, either invest in a different fund instead, or in an additional fund to supplement what is missing.