This is a typical example of American Tin Pan Alley-era novelty piano writing often found in early 20th-century sheet music. It is musically distinctive for its straightforward rhythmic drive and adherence to popular song structures of the 1910s.
The primary challenge is maintaining a steady, consistent rhythm within the ragtime-influenced syncopations.
Comparable difficulty and character — good candidates for what to learn next.
Big Chief Dynamite is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 2.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Big Chief Dynamite lasts about 3 minutes.
Big Chief Dynamite is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 'Way Down in Borneo-o-o-o by Al Piantadosi, Belgium Dry Your Tears by Al Piantadosi, Blumenwalzer by Léon Jessel — see the full similar-pieces list on this page.