As far as I'm aware, no such chronological account exists for the Boxer Uprising, at least not in English.

Probably the closest to what you're after is David J. Silbey's The Boxer Rebellion and the Great Game in China (2014), which mainly covers the theatre of fighting along the Tianjin-Beijing axis in 1900 and covers a bit of the occupation period. There's a heavy focus on Great Power politics and a bit on how colonial attitudes played into military action, and a reasonable degree of detail in military narrative though not quite a day-by-day, blow-by-blow account with statistics. What it doesn't really go into depth on is the Qing/Boxer side of the conflict, and there is basically nothing on Qing anti-Boxer campaigns in Shandong, the refusal of the southern provinces to support the Qing, or, critically, the vast Russian invasion of Manchuria in late 1900.

Said invasion is covered briefly in S.C.M. Paine's Imperial Rivals: China, Russia, and Their Disputed Frontier, 1858–1924 (1996), which is otherwise a general survey, mostly political and strategic, of Sino-Russian diplomacy in the stated period.

The classic study on the Boxers is Joseph Esherick's The Origins of the Boxer Uprising (1987), while there is also a more historiography- and theory-oriented work by Paul A. Cohen titled History in Three Keys: The Boxers as Event, Experience and Myth (1997) that's very good for anyone into that more theoretical side of things, but also IMO a suitable intro for the general reader, both to the Boxers and also some of the theory behind history writing – both of these have recommendations on the subreddit booklist, the former by /u/KippyPowers and the latter by myself.